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)
S safeer
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}

Preparation Products

Knockout NEET May 2023 (Easy Installments)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 5499/-
Buy Now
NEET Foundation 2023

-Adaptive Time Table -450 hours of Video Lectures -NCERT Solutions -CBSE Previous Year Papers -Chapter wise Tests.

₹ 14999/-
Buy Now
NEET Foundation + Knockout NEET 2025

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 34999/-
Buy Now
Knockout JEE Main April 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
Buy Now
Knockout NEET Aug 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
Buy Now
Boost your Preparation for JEE Main with our Foundation Course
 
Exams
Articles
Questions