The waiting time, in hours, between successive speeders spotted by a radar unit is a continuous random variable with cumulative distribution function f(x) = 0, x< 0, 1 − e −8x, x≥ 0. find the probability of waiting less than 12 minutes between successive speeders (a) using the cumulative distribution function of x; (b) using the probability density function of x.

The probability of waiting less than 12 minutes between successive speeders using  cumulative distribution function of x and using the probability density function of x are respectively; 0.7981 and 0.7981

The  cumulative distribution function of the random variable X, the waiting time, in hours, between successive speeders spotted by a radar unit is:

A) We want to find the probability of waiting less than 12 minutes between successive speeders. 12 minutes is also 12/60 hours = 0.2 hours

Using Cumulative distributive function, the probability is:

P(x < 20) = 1 - at x = 0.2

Thus;

P(x < 20) =

P(x < 20) = 0.7981

B) Using  probability density function of X is:

This gives;

P(x < 20) = between the boundaries of 0.2 and 0

Integrating gives;

P(x < 20) =

Solving this gives us;

P(x < 20) = 0.7981

Read more about cumulative probability distribution at; link

0.0076, if you meant 4.125 divided by 0.03125 it would be 132

step-by-step explanation:

first you have to move the decimal in 0.03125 over until its behind the 5 which is 5 places over. now the number is 3125

then you have to move the decimal in 4.125, 5 places over. now the number is 4,112,500.

now you divide like you would normally would and get 0.0076

multiplication is multiplication.   it might feel harder depending on what level of math you are in, but generally it will be the same old stuff, while implementing some new concepts and methods of solving work.