Question

Question 2: Let X be a random variable with the following probability density function (pdf): $f_x(x) = egin{cases} rac{x}{2}, & 0 < x < 1 \ \frac{3}{4}, & 1 \le x \le 2 \ 0, & \text{otherwise} \end{cases}$ a. Write the cdf of X. b. Calculate E(X) and Var(X). c. Calculate P(X ? 1.2) and P(X ? 0.5) d. Calculate P(X ? 1.2|X ? 0.5)

          Question 2: Let X be a random variable with the following probability density function (pdf):
$f_x(x) = egin{cases} rac{x}{2}, & 0 < x < 1 \ \frac{3}{4}, & 1 \le x \le 2 \ 0, & \text{otherwise} \end{cases}$
a. Write the cdf of X.
b. Calculate E(X) and Var(X).
c. Calculate P(X ? 1.2) and P(X ? 0.5)
d. Calculate P(X ? 1.2|X ? 0.5)

Question 2: Let X be a random variable with the following probability density function (pdf):
fx(x) = egincases racx2, 0 < x < 1 (3)/(4), 1 ≤ x ≤ 2 0, otherwise
a. Write the cdf of X.
b. Calculate E(X) and Var(X).
c. Calculate P(X ? 1.2) and P(X ? 0.5)
d. Calculate P(X ? 1.2|X ? 0.5)

Added by Theresa H.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Hoan Nguyen

12/23/2023

Step 1

The CDF of X, denoted as F(x), is given by: F(x) = ∫[0,x] f(x) dx Since the pdf f(x) is defined as 1/x^2 for 0<x<1 and 0 otherwise, the CDF can be calculated as follows: For x<0: F(x) = 0 For 0≤x<1: F(x) = ∫[0,x] 1/x^2 dx = [-1/x] from 0 to x = -1/x + 1 For x≥1: Show more…

Show all steps

Thanks for your feedback!

Question 2: Let x be a random variable with the following probability density function (pdf): xE(x)Var(x)P(x<=1.2)P(x>=0.5)P(x<=1.2|x>=0.5) Question 2: Let X be a random variable with the following probability density function (pdf) 0<x<1 fxx)= 1x2 0,otherwise a.Write the cdf of X. b.Calculate E(Xand Var(X) c.Calculate P(X1.2and PX0.5 d.Calculate P(X1.2|X0.5)