Let X∼Bin(6,0.7) and set Y=(X−2)^2 . Find P(Y=1).
P(Y = 1)
= P((X - 2)^2 = 1)
= P(X-2 = 1 or -1)
= P(X = 3 or X = 1)
= P(X = 1) + P(X = 3)
n = 6 , p = 0.7
P(X = 1) = 6C1 0.7 * 0.3^5
=6 * 0.7 * 0.3^5
= 0.010206
P(X = 3) = 6C3 * 0.7^3 * 0.3^3
= 20* 0.7^3 * 0.3^3
= 0.18522
hence required probability
= 0.18522 + 0.010206
= 0.195426
Please rate
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