Question

A. What is the cumulative distribution of X for the lifetime of a new Apple iPhone7GS (measured in years)?

b. Find P(X > 1), where X represents the lifetime of the iPhone.

Answer 1

The lifetime of a new Apple iPhone7GS follows an exponential distribution. The cumulative distribution function is given as P(X < x) = 1 - e^(-λx). The average lifetime is three years, so λ = 1/3. To find the cumulative distribution of X for the iPhone, substitute the value of x into the cumulative distribution function. To find P(X > 1), use the complement of P(X < 1).

Step-by-step explanation:

The lifetime of a new Apple iPhone7GS follows an exponential distribution. The cumulative distribution function is given as P(X < x) = 1 - e^(-λx), where λ represents the rate parameter. In this case, the average lifetime is three years, so λ = 1/3. To find the cumulative distribution of X for the lifetime of the iPhone, we substitute the value of x into the cumulative distribution function:

P(X < x) = 1 - e^(-1/3x).

For part b of the question, we need to find P(X > 1). This is the complement of P(X < 1), which can be found by substituting x = 1 into the cumulative distribution function:

P(X > 1) = 1 - P(X < 1) = 1 - (1 - e^(-1/3)).