Question

3. Let X be a continuous random variable with the following cumulative probability distribution function for some real constants a, b: \begin{equation} F_X(x) = \begin{cases} 0 & x \le -1 \\ a(x+1)^2 & -1 < x \le 0 \\ 1 + b(1-x)^2 & 0 < x \le 1 \\ 1 & x \ge 1 \end{cases} \end{equation} If we further know that E(X) = 0, then find the constants a, b. What is the probability density function of X?

          3. Let X be a continuous random variable with the following cumulative probability distribution function for some real constants a, b:
\begin{equation*}
F_X(x) = \begin{cases} 0 & x \le -1 \\ a(x+1)^2 & -1 < x \le 0 \\ 1 + b(1-x)^2 & 0 < x \le 1 \\ 1 & x \ge 1 \end{cases}
\end{equation*}
If we further know that E(X) = 0, then find the constants a, b. What is the probability density function of X?

3. Let X be a continuous random variable with the following cumulative probability distribution function for some real constants a, b:

FX(x) = 0 x ≤ -1
a(x+1)^2 -1 < x ≤ 0
1 + b(1-x)^2 0 < x ≤ 1
1 x ≥ 1

If we further know that E(X) = 0, then find the constants a, b. What is the probability density function of X?

Added by Janet R.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sri K

02/23/2023

Step 1

Step 1: We are given the cumulative probability distribution function (CDF) of X as follows: F(x) = 0, for x < 0 F(x) = ax, for 0 ≤ x < 1 F(x) = 1, for x ≥ 1 Show more…

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3. Let X be a continuous random variable with the following cumulative probability distribution function for some real constants a,b (0 x-1 05x>I- 1+b1-x0<x1 1 1 w further know that E(X)=0, then find the constants a,b.What is the probability density function of X?