Jiahui is experimenting with a coin that is biased. Each time Jiahui flips the coin, the probability of getting a head is P(H)=0.61.
Each flip is independent of the other flips.
(a) In a game, Jiahui flips the coin 8 times. Let X be the total number of times the coin shows a head out of 8 flips.
Find the following probabilities. Enter your answers below correct to at least 3 significant figures.
(i) Find the probability of getting exactly 2 heads: _____.
(ii) Find the probability of getting at most 2 heads: ______.
(iii) Find the probability of getting more than 2 heads: ______.
(b) We now want to compute the expected value and variance of X. Enter your answers below as exact values.
(i) The expected value, μₓ​= _______.
(ii) The variance, σ²ₓ= ____.