Question

2. Let X be a discrete random variable with the following PMF PX(k) = { 0.5 for k = 1; 0.3 for k = 2; a for k = 3; 0 otherwise } (a) Find the value a so that PX(k) is a valid PMF. (b) If Y =2/X, find EY.

Name: 2 let x be a discrete random variable with the following pmf pxk 05 for k 1 03 for k 2 a for k 3 0 otherwise a find the value a so that pxk is a valid pmf b if y 2x find ey 65016
Uploaded: 2023-11-26T11:43:56-08:00
Duration: 2 min 35 s
Channel: Robin Corrigan
Description: 2 let x be a discrete random variable with the following pmf pxk 05 for k 1 03 for k 2 a for k 3 0 otherwise a find the value a so that pxk is a valid pmf b if y 2x find ey 65016

          2. Let X be a discrete random variable with the following
PMF
PX(k) = { 0.5 for k = 1;  0.3 for k = 2;  a for k =
3;  0 otherwise }
(a) Find the value a so that PX(k) is a valid PMF.
(b) If Y =2/X, find EY.

Added by Nicholas B.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Robin Corrigan

11/26/2023

Step 1

So, we have: $$ 0.5 + 0.3 + a + 0 = 1 $$ Solving for a, we get: $$ a = 1 - 0.5 - 0.3 = 0.2 $$ So, the PMF is: $$ P_X(k) = \begin{cases} 0.5 & \text{for } k = 1 \\ 0.3 & \text{for } k = 2 \\ 0.2 & \text{for } k = 3 \\ 0 & \text{otherwise} \end{cases} $$ (b) Show more…

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2. Let X be a discrete random variable with the following PMF PX(k) = { 0.5 for k = 1; 0.3 for k = 2; a for k = 3; 0 otherwise } (a) Find the value a so that PX(k) is a valid PMF. (b) If Y =2/X, find EY.