Answer to Question #153612 in Statistics and Probability for nitin sher

Question

A shipment of 8 similar microcomputers to a retail outlet contains 3 defectives. If a school makes a random purchase of 2 of these computers, nd the probability distribution for the number of defectives. also obtain the cumulative probability distribution.

Answer 1

$p = \frac{3}{8} = 0.375$

n = 2

X ~ Bin(n, p)

X takes value 0, 1, 2

P(X=x) = ⁿC_xp^x(1-p)^n-x

P(X=0) = ²C₀0.375⁰(1-0.375)^2-0

$= \frac{2!}{0!2!}(0.375)^0(0.625)^2 \\ = 0.390625$

P(X=1) = ²C₁0.375¹(1-0.375)^2-1

$= \frac{2!}{1!1!}(0.375)^1(0.625)^1 \\ = 0.468750$

P(X=2) = ²C₂0.375²(1-0.375)^2-2

$= \frac{2!}{2!0!}(0.375)^2(0.625)^0 \\ = 0.140625$

Probability distribution of X:

F_x(0) = 0.390625

F_x(1) = P(X=0) + P(X=1) = 0.390625 + 0.468750 = 0.859375

F_x(2) = F_x(1) + P(X=2) = 0.859375 + 0.140625 = 1

Cumulative probability distribution: