The following gambling game has been proposed, which a player must pay to play. First, a value U is chosen uniformly from the set [0, 10]. Next, a number is chosen according to a Poisson random variable with a parameter U. Letting X be the number chosen, the player receives $X. Find E[X], which is the amount a player should pay to make this a fair game HINT: Use the Law of Total Probability for Expectations, E[X]

The player should be required to pay $5 to make this a fair game.

Step-by-step explanation:

U ~ Uniform(0, 10)

E[U] = (0 + 10)/2

         = 5

X | U ~ Poisson(U)

E[X | U] = U

By law of total probability for expectations,

E[X] = E[E[X|U]] = E[U] = $5

Therefore the player should be required to pay $5 to make this a fair game.

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.

only 10/60 isn't equivalent

hope this : )