Answer
Find out the how many games did the teams lose .
To prove
Formula
As given
Salem High School's winter sports teams WON 72% of their games last season.
If the teams played 50 games .
Percentage = 72%
Total value = 50
Put in the formula
Number of games win = 36
Number of games teams loses = Total number of games - number of games win
= 50 - 36
= 14
Therefore the number of games team loses are 14 .
Answer:
See the proof below.
Step-by-step explanation:
Assuming this complete question: "For each given p, let Z have a binomial distribution with parameters p and N. Suppose that N is itself binomially distributed with parameters q and M. Formulate Z as a random sum and show that Z has a binomial distribution with parameters pq and M."
Solution to the problem
For this case we can assume that we have N independent variables with the following distribution:
bernoulli on this case with probability of success p, and all the N variables are independent distributed. We can define the random variable Z like this:
From the info given we know that
We need to proof that by the definition of binomial random variable then we need to show that:
The deduction is based on the definition of independent random variables, we can do this:
And for the variance of Z we can do this:
And if we take common factor we got:
And as we can see then we can conclude that