Question

Please include steps.

Let x be a binomial random variable with n=4 and p=0.8. Find the following. P(X = 3) P(X < 4)

Answer 1

Using Binomial Distribution :
P( x = X) = b(X ; n,p) = px (1 - p)n-x

Now , P( x = 3) = (0.8)3 (1 - 0.8)4 - 3
= (0.8)3 (1 - 0.8)4 - 3
= [(4 * 3!) / 3!] (0.8)3 (1 - 0.8)4 - 3
= 4* (0.8)3 (1 - 0.8)4 - 3
= 4* (0.8)3 (0.2)
= 4* (0.512)* (0.2)
= 4* (0.1024)
P( x = 3) = 0.4096

Now , P(x < 4) = 1 - P( x = 4)
= 1 - (0.8)4 (1 - 0.8)4 - 4
= 1 - (0.8)4 (1 - 0.8)4 - 4

= 1 - (0.8)4 (1 - 0.8)4 - 4

= 1 - 1(0.8)4 (0.2)0
= 1 - (0.8)4
= 1 - 0.4096
P( x < 4) = 0.5904

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