Question

You will flip two coins together 10 times. You are interested in the outcome where both coins land on heads. Let X be the number of times you observe this outcome. Answer Question 1 through 4.

1. What are the possible values for x? (values the random variable X can take)

2. Is X binomial random variable? If so, state its parameter n and p. If not, explain why.

3. Find the probability that you will see both coins landing on heads at least once. Round your answer to the three decimal places.

4. Find the mean and the variance of X

Answer #1

X = number of times both coins lands on head.

**1)** Possible value of X = 0, 1, 2, 3, ...., 9,
10 because it's possible that this doesn't happen and this is also
possible that we get both heads on all 10 times.

**2)** This is Binominal distribution with n = 10
and p = 1/4.

p = probability of success = probability of getting both head = 1/4

**3)** P(at least once) = 1 - P(X = 0)

**4)** mean = n*p = 10*(1/4) =
**2.5**

Variance = n*p*q = 10*(1/4)*(1-1/4) = **1.875**

Please comment if any doubt. Thank you.

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