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An inveslment counselor calls with hot stock tip He believes that it the economy rCrrains strong Ihe investment will resul

Question:

An inveslment counselor calls with hot stock tip He believes that it the economy rCrrains strong Ihe investment will resul in prafit of 540,J0O Ithe economy grows at a moderate the Investnent will restii 2 pron & 520,000 However if the economy gces into recession, Lhe investment wi resutt loss of 540,000. You contacl ecanomisl wha believes Ihere 20%0 probab ity the economy wil remain strong 6096 probabiliyy Me econoal} Orow Modetaie pace , 2090 probab llty the BCOnomv will slip into recession What Is ine expected Eoft fom Ihi; inveshment? The expected profit is (Type an integer or & decimal )


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Investment An investment counselor calls with a hot stock tip. He believes that if the economy remains strong, the investment will result in a profit of 50,000 dollar. If the economy grows at a moderate pace, the investment will result in a profit of 10,000 dollar. However, if the economy goes into recession, the investment will result in a loss of 50,000 dollar. You contact an economist who believes there is a $20 \%$ probability the economy will remain strong, a $70 \%$ probability the economy will grow at a moderate pace, and a $10 \%$ probability the economy will slip into recession.

What is the expected profit from this investment?

.

Here in this problem, the required probability p required can be calculated as so. I will just put all the value years. So first I will write The value of the first stop will increase in value at least 10% within next year. So I can write it as p one multiplication P two, which is the second stop, will increase in the value at least 10% within next year. Multiplication Petri, which is the Kurdish talk with increasing the value at least 10% within next year.

So now I'm just putting all the value which are given in the question. So I can write 0.7 multiplication 0.55 multiplication 0.20. And on calculating it, I get the final answer average 0.77 Hence probability that all three stew increases at least 10% is 0.0 7/7. This probability is very small. Hence it is unusual for all three sto to increase at 10% rate.

So I hope you understand the solution as how I solve this problem and c a d concept with it..

So on the left over here, I have the data set that we're interested in a forecast of GDP growth in America based on economist. So we're first asked to finding the minimum value in this series. And I went ahead and reordered these. This Siri's just so it's easier for me to visualize and see what exactly is going on with this data, because I reordered it. I was able to find the minimum value really easily.

The minimum value would be the first, uh, value here. So 0.4. Okay, So at 0.4 and it was really easy to see the maximum value again because I already reordered this data and I have the value of 3.5 as my max over here, so Oh, that doesn't look good. My max is three point five. That doesn't look great either, but we'll continue.

So, my mean is going to be the sum of all my observations over the number of my observations. So if you count out all of these, all the number of observations you're going to get that your end is equal to 30 okay? And then you're going to get that the sum of all observations. This is a fancy way of writing. The sum is equal to ah, 69. So you're mean is going to be the result of 69 over 30 which is approximately equal to 2.3.

So you're mean is about 2.3 now for your median? Ah, you're just basic. Or I would just start crossing from the top or bottom. Or what you can do is, uh, find the the exact value in which the median lies. So you can take because the medium is the 50th percentile. You can take 50 over 100 which is 1000.5, take 50 over 100 and then multiply it by the end, which we figured out was 30 and that is equal to 15.

So because that is an even number we're going to or an integer we're going to take the value in between 15 and 16 or the values of 15 and 16 and take the average of them. So here is the value of index. At 15 the value index that 16 is 2.5, both of them are 2.5. So we're going to take the average of the 22.5 plus 2.5 divided by two is equal to 2.5. So we get that our median is 2.5.

Okay, Now our mode, we're basically going to scan through our data set and figure out which data point which individual point occurs most frequently. Okay? And we find that the the the value with the most that is most frequent is 2.7, So I remote is 2.7. Okay? Now, to find out my first and third corps tiles, I'm basically going to do the same thing I did for the median. OK, I will take 25 divided by 100 which I know is 1000.25 and multiply by my end, which is 30 which is equal to 70.5 7.5. Sorry, not 70.57 point five.

Okay. And that means I'm going to take the value at the eighth index and the seventh index and average them. Okay, so 12345123456 seven. Okay, so seven is 1.9 and eight is, too. So I'm going to take the average between 1.9 and two and divide by two, which yields 1.95 Okay, all right.

And now we're going to do the same thing for the 75th percentile or ah, the third quarter mile. Okay, take the ah percentile in decimal form. Multiply it by my end, which is 30 which yields 22.5. Okay, and this appears should not be an equal sign. That should be an arrow.

Um, because those two aren't equally each other. So I'm going to find the 22 23rd indices and average them. Okay, so I'm going to count 1231234 all the way down until I get until I get to 2.8 and 2.8 and the average of 2.8 and 2.8 is 2.8. So I get that. My 75th quartile is 2.8.

Now. This question about whether the economists are optimistic or pessimistic about economic outlook depends on how you view optimism and pessimism. But because all of these data points are positive, that means that there's economists forecast a growth in GDP, which is a good thing. So I would say that there is a positive outlook provided by the economists. Thanks for watching.

We're told that on a given day, 30% of the stocks that make up the Dow Jones industrial average went up, and the financial analyst claims that the Dow Jones is representative of the overall stock market in there. For 30% of the stocks in the New York Stock Exchange are expected to go up part A were as to make hypotheses test this claim. Some no hypothesis is that the proportion of the New York Stock Exchange stocks that went up on the day is 0.30 and therefore the alternative is that the precaution is not 0.30 And then in Part B. We're told that we have a sample of 50 stocks from the New York Stock Exchange. We know that N is equal to 50 and that of these 50 stocks, 24 went up and were asked to give a point estimate of the proportion that went up for the New York Stock Exchange.

So the best estimate of proportion in this case is the sample proportion itself. The sample proportion is simply 24 divided by 50 or 48% and in part C, we're given an Alfa level of 0.1 and whereas to draw conclusions regarding the hypothesis test. So the test statistic here is the SAT score, because sample proportions are approximately normally distributed. We have said Equal to you comes out of 2.78 So if we take a look at where this stands on a normal standard, normal distribution, 2.78 is way out here, way out in the upper tail. And so, since this is a two sided test, are key value is the area in the upper tail as the will is the area in the lower tail? So that's the ear into the left of minus 2.78 so we can look this up in a set table by looking up minus 2.78 That will give us the air in the lower tail, and then we simply have to double it to get her the Peace Corps RPI value.

So let's look this up in the table minus 2.78 is right here. Moving on here for over two is equal to 0.27 tells us that RPI value is equal to zero point 0054 and then to draw a conclusion, we just have to compare the P value to Alfa, so it's quite clear to see that 0.54 is less than 0.1 so therefore we can reject the null hypothesis..

So we want to know the behavior of the stock markets crashed between 19 uh, 20 to 1929. This is a It's a natural function, and it's prohibitive will be this formula. So we have white crime. This is a constant soapy zero, and it's the X will be to the X Times ln off a chance, 1 to 4. So, um, from this trip, if we can see that war and see our function was locus going to be positives are function.

F is going to be increasing positive for all of the X is greater than or equal to one. So from the beginning, which is 1920 all the way, So it doesn't really our function or this stock index will be increasing. Okay, Now we want to do the second derivative eye level time. It's going to be able to, uh, see same idea. This here is a constant.

So this is what we're taking the derivative off. So we have, uh then out of that, we have a to the oak. So which is 1.2 to 4 to the X in l f A a. Just pointing to four time selling off 1.224 Unless you combine this, we get 1.2 to 4 to the ex. I'm selling off Venice squared off, huh? 1.224 And similarly, is he that were, uh, dysfunction is also increasing.

That this is something primitive is also positive for all of the exits guarded than or equal to zero. OK, but are equal to one. So this means that I will function all right f for why so If is increasing at an increasing rate. And so, um, basically, in stock market context, wth e stocks are being over prized. So every year the prize of this talks the price to buy a stock is going up at a higher rate.

By the way in which the stock market prices going up, it's higher every year. And so this is unattainable because the I guess the higher the prices get, the less people that are able to buy stocks eso it would be unattainable or unsustainable. Okay. And we want to know. I guess what would be 1920 14.

So from 1920 2014 or with these type mark price would be using the model we have so sends, uh, 2014 minus and 20 days and Gilles at night before. So our X, or our time is equal to 94 just want a plaid Isn't original function, which is, uh, c f or why, off 94 which is going to give us 40 points and the one plus 1.224 to the 94. And this gives us, uh, surprise index of sap price index off, see? 178,000,000 of 4000 and 24 100 and, uh, 21 dollars and 80 to be sense approximately. Okay, so in, I guess in 2019 if the prizes will kept rising at the rate which they do on I guess the price index, the amount you will need to purchase the stock would reach up to $180,000,000. And again, that is definitely unsustainable because of average person will not be able to buy the stocks.

So, yeah, that's a.

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