a) On a particular trading day, you are going to buy shares of the stock that is the cheapest. Find the probability density function for the price per share Y that you will have to pay. f(y) = e-(y-5) b) From part (a), find the expected value for the price per share that you will have to pay. Enter the exact value. Hint: You could use integration by substitution with t = y-5 and then use the properties of the exponential density (such as its density integrates to one and its expected value), or integration by parts.

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answer only part b . 

The opening prices per share of three similar stocks X1, X2, X3 are independent random
variables, each with density function
(-5)
if a2 5
f(x) = { 3
else
a)
On a particular trading day, you are going to buy shares of the stock that is the cheapest. Find the
probability density function for the price per share Y that you will have to pay.
f(y) = e-(y-5)
b)
From part (a), find the expected value for the price per share that you will have to pay. Enter the exact
value.
Hint: You could use integration by substitution with t = y - 5 and then use the properties of the
exponential density (such as its density integrates to one and its expected value), or integration by
parts.
Transcribed Image Text:The opening prices per share of three similar stocks X1, X2, X3 are independent random variables, each with density function (-5) if a2 5 f(x) = { 3 else a) On a particular trading day, you are going to buy shares of the stock that is the cheapest. Find the probability density function for the price per share Y that you will have to pay. f(y) = e-(y-5) b) From part (a), find the expected value for the price per share that you will have to pay. Enter the exact value. Hint: You could use integration by substitution with t = y - 5 and then use the properties of the exponential density (such as its density integrates to one and its expected value), or integration by parts.
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