Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • A discrete random variable X has the following probability distribution : X 0 1 2 3

A discrete random variable X has the following probability distribution :

X 0 1 2 3 4 5
P(X) 4C2 3C2 2C2 C2 C 2C

(a) Find the value of C.

(b) Find the mean of the distribution.

(c) Given \sum x_{i}^{2} p_{i} = 14, find the variance of the distribution.

 

 
 
 
 
 

Answers (1)

X 0 1 2 3 4 5
P(X) 4C2 3C2 2C2 C2 C 2C
X.P(X) 0 3C2 4C2 3C2 4C

10C

(a)

\sum P(x)=1

4C^2+3C^2+2C^2+C^2+C+2C=1

10C^2+3C-1=0

10C^2+5C-2C-1=0

5C(2C+1)-1(2C+1)=0

(2C+1)(5C-1)=0

C =\frac{1}{5}  C = -1/2 (Negative probability is not possible)

Hence the value of C =\frac{1}{5}.

(b) Mean of the distribution.

\\$Mean$ = \sum XP(X) = 10C^2 + 14C \\ =10 \times \frac{1}{25} + 14 \times \frac{1}{5} \\\\ = \frac{16}{5}

(c) Given:

\sum x_{i}^{2} p_{i} = 14

\\$Variance $ = \sum x_{i}^{2} p_{i} - \left(\sum XP(X)\right)^2 = 14 - (\frac{16}{5})^2 \\\\ = \frac{94}{25}

Posted by

Safeer PP

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Class 12 board exams 2025 to have 50% competency-based questions; no change in 10th
anam-khan

CBSE Class 12 board exams 2024 over; expected result date, trends of last 10 years
anam-khan

CBSE Class 12 accountancy board exam analysis 2024 out; paper rated easy, balanced

Latest Question