Question

Graph this distribution in R studio, please! Assume that a component passes a test is 0.85 and that components perform independently.  What is the probability that the third failure will occur on the tenth component tested?

Answer 1

The probability of success is .

The PMF of the number of components tested till 3rd failure occurs has Negative Binomial distribution.

The PMF is

The required probability is

Use RStudio to plot the PMF. Code below.

plot(1:1)
dev.new()
Y <- 0:17
plot(Y,dnbinom(Y,size=3,prob=0.15), type="h", col="blue", lwd=2, xlab="Y", ylab = "P(Y=y)", main="PMF of Y")