Let X have a binomial distribution with n 20 and p 040 Fin

Let X have a binomial distribution with n = 20, and p = 0.40). Find: Let X be a random variable with Poisson distribution and parameter value of 4. Find the following:

Solution

X is binomial with (20,0.40)

P(X=r) = 20Cr (0.40)^r 0.60 ^(20-r)

i) P(X=5) = 0.07465

ii) P(X<=5) = P(x=0 or 1 or...5) = 0.1256

iii) P(3<x<=8) = P(X<=8)-P(X<=3)

= 0.5956-0.0160

= 0.5796

iv) P(X>=8)=0.58411

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3) X is poisson with mean = 4

P(3<x<7)= P(x<7)-P(X<3)

= 0.8896-0.2381

= 0.6515

P(X<=5)=0.7851