Question

Adults should get a booster dose of the Td (tetanus and diphtheria) vaccine every 10 years. Suppose the length of time (in years) that the vaccine provides protection has an exponential distribution with a mean of 15 years. (a) Find the value of λ for this distribution.

Answer 1

The value of λ for the exponential distribution representing the length of time the Td vaccine provides protection every 10 years is 0.0667 years^-1.

Step-by-step explanation:

The exponential distribution is usually defined as f(x|λ) = λ * exp(-λx) for x >= 0, where λ is the rate parameter.

In this case, we are given that the mean of the exponential distribution is 15 years.

The mean of an exponential distribution is equal to 1/λ.

So, 1/λ = 15 years.

Now, solve for λ:

λ = 1/15 = 0.0667 years^-1