The Bern distribution models a single experiment with two outs Namely, it has one parameter and takes valor 1 with probability and takes valor with probability - Fie example, if yim are modeling whether or not a single cutoure will purchase a product, and that individual has purchase probability r, then you can model her purchasing decisions Bertol nodon variable Let X be a random variable that fillows a Bermonili distribution with morese probability. Answer the following questions and shume all work, explaining och step.
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The Bern distribution models a single experiment with two outs Namely, it has one parameter and takes valor 1 with probability and takes valor with probability - Fie example, if yim are modeling whether or not a single cutoure will purchase a product, and that individual has purchase probability r, then you can model her purchasing decisions Bertol nodon variable Let X be a random variable that fillows a Bermonili distribution with morese probability. Answer the following questions and shume all work, explaining och step.
a. What are the possible values that X can take? This is called the support of the random
variable.
b. What is the expected value of X? Show all work, by explaining how to calculate
X∞
i=−∞
xi
· P(X = xi).
c. What is the variance of X? Again, show all work, by explaining how to calculate the variance
from the formula
X∞
i=−∞
(xi − E(X))2
· P(X = xi).
d. The Bernoulli distribution is related to the Binomial distribution. Let Y be a random variable
that follows a Binomial distribution. As we dsicussed in class, the Binomial distribution has
two parameters, n and π. For what values of n and π will Y have the same distribution as
X? Explain.