Question

1. A continuous random variable X has the cumulative distribution function (cdf) below: $F(x) = egin{cases} 0 & : x < 0 \ frac{(9-2x)x^2}{27} & : 0 le x le 3 \ 1 & : x > 3 end{cases}$ (a) Calculate P(X > 2) (b) Find the probability density function (pdf) of X. (c) Calculate E[X$^2$]

          1. A continuous random variable X has the cumulative distribution function (cdf) below:
$F(x) = egin{cases} 0 & : x < 0 \ frac{(9-2x)x^2}{27} & : 0 le x le 3 \ 1 & : x > 3 end{cases}$
(a) Calculate P(X > 2)
(b) Find the probability density function (pdf) of X.
(c) Calculate E[X$^2$]

$1. A continuous random variable X has the cumulative distribution function (cdf) below: F(x) = egincases 0 : x < 0 frac(9-2x)x^227 : 0 le x le 3 1 : x > 3 endcases (a) Calculate P(X > 2) (b) Find the probability density function (pdf) of X. (c) Calculate E[X^2]$

Added by Michele L.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Madhur L

07/13/2023

Step 1

Calculate P(X > 2) Since we want to find the probability that X is greater than 2, we can use the complementary rule: P(X > 2) = 1 - P(X ≤ 2). From the given CDF, we know that F(2) = 0. So, P(X > 2) = 1 - 0 = 1. Show more…

Show all steps

Thanks for your feedback!

A continuous random variable X has the cumulative distribution function (CDF) below: F(z) = 0, for z < 1 (9-2z)/2, for 1 ≤ z < 3 1, for z ≥ 3 Calculate P(X > 2). Find the probability density function (PDF) of X. Calculate E(X^2).