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:

-1/2 +2

step-by-step explanation:

the data of the detroit pistons in numerical order from least to greatest is 0.30, 0.37, 0.55, 0.62, 0.69, 0.72, 0.73, 0.75, 0.77, 0.78, 0.80, 0.81, 0.81, 0.83, 0.84, 0.89

the data of the miami heat in numerical order from least to greatest is 0.50, 0.50, 0.56, 0.57, 0.67, 0.72, 0.72, 0.72, 0.75, 0.75, 0.76, 0.81, 0.82, 0.90, 1.00, 1.00

the detroit pistons median : 1.52

the miami heat median: 1.47

the iqr of this data is 0.05