A fair coin is flipped 3 times. Let X be the number of heads in the 3 tosses. (1) Find the pmf for X;

(2) calculate the expected value of X.

1)

P(X = 0) = 0.125

P(X = 1) = 0.375

P(X = 2) = 0.375

P(X = 3) = 0.125

2)

E(X) = 1.5

Step-by-step explanation:

For each coin, there are only two possible outcomes. Either it is heads, or it is tails. The probability of a toss being heads or tails is independent of any other toss. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

The expected value of the binomial distribution is .

A fair coin is flipped 3 times.

Fair means that it is equally as likely to be heads or tails, so .

3 times means that

(1) Find the pmf for X;

Probability of each outcome. So

(2) calculate the expected value of X.

b. 1.25 hr

step-by-step explanation:

if you have a constant speed of 60 mph, then you have a ratio between 60 mi. to 1 hr. dividing both sides by 60 we get the ratio

1 mi. to

then mult. both sides by 75 we get the ratio

75 mi. to

simplifying we get

75 mi. to

or 1.25 hr.

not sure but it may be b, as i said i'm not sure.