Let x be a binomial random variable based on n trials and a success probability of px; let y be an independent binomial random variable based on m trials and a success probability of py. find e(w) and var(w), where w=4x+6y.

Step-by-step explanation:

For this case we have the following distributions given:

The expected value for x is

And the variance

The expected value for x is

And the variance

We define a new random variable:

We need to find the expectd value and the variance for W.

For the expected value we have this:

And if we replace the parameters we got:

Now foe tha variance of W we know that X and Y are indpenendet variable so then

For this case we can use the property that is a is a constant and X a random variable then , and we got this:

And if we replace we got:

a) y = -3x +2

b) y = 1/2x -6

these 2 can be combined into one equation.

-3x +2 = .5x -6

8 = 3.5x

x = 8 / 3.5 = 2.2857142857

y = -3 * (8 / 3.5) +2

y = (-24 / 3.5) + 2

y = -4.8571428571

step-by-step explanation: