Question

Asked May 13, 2019

18 views

Step 1

The given information is not sufficient to solve all the subparts. More information is required to solve Part (G). So, we will answer first two subparts.

Step 2

**E) Obtaining the probability distribution of X:**

It was found that 20% of the time, Melvin misses and does no damage, 70% of the time he hits and does 8 damage and 10% of the time he hits and does 12 damage.

The random variable *X *denotes the amount of damage Melvin does in a single swing.

That is, the random variable *X *takes values 0, 8 and 12 with probabilities 0.20(=20%), 0.70(=70%) and 0.10(=10%) respectively.

The probability distribution of a random variable *X *is the set of all possible values of the random variable *X *and its corresponding probabilities.

From the given information, the probability distribution of *X *is obtained and is given in the following table:

Step 3

**F) Obtaining the mean, variance and standard deviation of X:**

The mean value of a discrete random variable *X *is given by,

E(*X*) = µx = ∑*x*.P(...

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