Question

A random variable is uniformly distributed over the interval 2 to 10 . Find it's varience​

Answer 1

Answer:

A random variable X, which is uniformly distributed over an interval [a, b] i.e. X ~ U(2, 10) is given by ;

f(x) = 1/(b-a) , x ∈ [a, b] and f(x) = 0 , elsewhere. Here, given a = 2 and b = 10 ==> (b-a) = 10 - 2 = 8 . Now,

E(x) = ∫₂¹⁰(x.f(x))dx = (1/8)[x²/2]₂¹⁰ = (1/16)(100 - 4) = 6 . And

E(x²) = ∫₂¹⁰(x².f(x))dx = (1/8)[x³/3]₂¹⁰

= 124/3 . Therefore, variance V is given by

V = E(x²) - {E(x)}² = (124/3) - 36 = 16/3.

Step-by-step explanation:

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