Assume that the random variable X follows a binomial distribution with n = 5 and

Question

Assume that the random variable X follows a binomial distribution with n = 5 and p = 0.5. (That is, equivalently, assume that X is the process of flipping a fair coin five times.) Using either R (with functions dbinom () or pbinom ()), or calculating by hand using the binomial PDF below, answer the following questions. Show your code or your typed math. f(x; n, p) = (n x)p^x (1 - p)^(n - x) What is the probability of X = 3? (Equivalently, what is the probability of obtaining 3 heads in 5 flips of that fair coin?) What is the probability of X

Explanation / Answer

Result:

a).

Rcode:

px <- dbinom(3, 5, 0.5, log = FALSE)

px

R output

px <- dbinom(3, 5, 0.5, log = FALSE)

> px

[1] 0.3125

P( x=3) =0.3125

b).

R code

px <- dbinom(0, 5, 0.5, log = FALSE)+dbinom(1, 5, 0.5, log = FALSE)+dbinom(2, 5, 0.5, log = FALSE)

px

R output

px <- dbinom(0, 5, 0.5, log = FALSE)+dbinom(1, 5, 0.5, log = FALSE)+dbinom(2, 5, 0.5, log = FALSE)

> px

[1] 0.5

P( x <3) =0.5

c).

R code

px <- dbinom(4, 5, 0.5, log = FALSE)+dbinom(5, 5, 0.5, log = FALSE)

px

R output

px <- dbinom(4, 5, 0.5, log = FALSE)+dbinom(5, 5, 0.5, log = FALSE)

> px

[1] 0.1875

P( x 4) =0.1875

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