Question

The opening prices per share of three similar stocks X1, X2, X3 are independent random variables, each with density function f(x) = { 1/3e^-1/3(x-2) if x >= 2 0 else . On a given trading day you are going to buy shares of the stock that is the cheapest. Find the probability density function f for the price per share Y that you will have to pay. a, What's f (y) ? From part (a), find the expected value for the price per share that you will have to pay. Enter the exact value. b, What's the expected value ?

          The opening prices per share of three similar stocks X1, X2, X3 are independent random variables, each with density function
f(x) = { 1/3e^-1/3(x-2) if x >= 2
0 else .
On a given trading day you are going to buy shares of the stock that is the cheapest. Find the probability density function f for the price per share Y that you will have to pay.
a, What's f (y) ?
From part (a), find the expected value for the price per share that you will have to pay. Enter the exact value.
b, What's the expected value ?

The opening prices per share of three similar stocks X1, X2, X3 are independent random variables, each with density function
f(x) = 1/3e^-1/3(x-2) if x >= 2
0 else .
On a given trading day you are going to buy shares of the stock that is the cheapest. Find the probability density function f for the price per share Y that you will have to pay.
a, What's f (y) ?
From part (a), find the expected value for the price per share that you will have to pay. Enter the exact value.
b, What's the expected value ?

Added by Robin H.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sri K

02/26/2023

Step 1

Let Y = min(X1, X2, X3). We can find the cumulative distribution function (CDF) of Y and then differentiate it to find the probability density function (PDF). The CDF of Y is given by: P(Y <= y) = 1 - P(Y > y) = 1 - P(X1 > y, X2 > y, X3 > y) Since X1, X2, and Show more…

Show all steps

Thanks for your feedback!

The opening prices per share of three similar stocks X1, X2, X3 are independent random variables, each with density function f(x) = { 1/3e^-1/3(x-2) if x >= 2, 0 else On a given trading day you are going to buy shares of the stock that is the cheapest. Find the probability density function f for the price per share Y that you will have to pay. a, What's f (y) ? From part (a), find the expected value for the price per share that you will have to pay. Enter the exact value. b, What's the expected value ?