After a big win at the slot machine, a gambler stuffs his pockets with quarters and walks down the Las Vegas strip. Unfortunately, there is a hole in one pocket and the coins drop out randomly, at a rate of 5 per 50 meters. If you follow the gambler for 100 meters, what is the probability mass function for the number of quarters you find on the sidewalk, head up?

Step-by-step explanation:

Given That:-

After a big win at the slot machine, a gambler stuffs his pockets with quarters and walks down the Las Vegas strip. Unfortunately, there is a hole in one pocket and the coins drop out randomly, at a rate of 5 per 50 meters.

A gambler stuffs his pockets with quarters and walks down the Las Vegas strip.

Unfortunately, there is a hole in one pocket and the coins drop out randomly, at a rate of 5 per 50 meters.

λ = rate of finding a quarter = 5 (for 50 meters)

Now, for 100 meters, λ = 5 x 2 = 10.

If X = random variable denoting no. of quarter found on sidewalk, head up.

X - possion (λ = 10).

There the probability mass function = P (X = x) = e^{-λ} x λ^{x} / {x!}

= e^{-10} x {10^{x} / {x!}; x = 0, 1, 2, ... = is the probability mass function for the number of quarters you find on the sidewalk, head up.