Question

Is it possible to have a binomial distribution with (just write “YES” OR “NO”) Mean=5 & Variance = 2.5 P(X>1) = 1.27 P(X=3.8) = 0.29 P(X>1) = 0.35

Answer 1

Given : Mean=5 & Variance = 2.5

To find : possible or not  P(X>1) = 1.27 P(X=3.8) = 0.29 P(X>1) = 0.35

Solution:

Mean  = 5

Variance = 2.5

Mean = np   = 5

Variance = npq   = 2.5

=> 5q = 2.5

=> q = 0.5 = 1/2

p = 1 - q = 0.5 = 1/2

np = 5

=> n(1/2) = 5

=> n = 10

P(X) = ⁿCₓpˣqⁿ⁻ˣ

P(X > 1)     = 1.27  not possible as probability can not be greater than 1  

P(X > 1)   = 1  -  P(0) - P(1)

= 1 -   ¹⁰C₀(1/2)⁰(1/2)¹⁰ - ¹⁰C₁(1/2)¹(1/2)⁹

=  1  -  11 /2¹⁰

=  0.989

P(X>1) = 0.35  ( wrong)

P(x = 3) = 0.117

P(X = 4) = 0.2

Henc P(x = 3.8) can not be 0.29

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