Suppose 4 Bernoulli trials, each with success probability p, are conducted such that the outcomes of...

Suppose 4 Bernoulli trials, each with success probability p, are conducted such that the outcomes of the 4 experiments are mutually independent. Let the random variable X be the total number of successes over the 4 Bernoulli trials.

(a) Write down the sample space for the experiment consisting of 4 Bernoulli trials (the sample space is all possible sequences of length 4 of successes and failures you may use the symbols S and F).

(b) Give the support (range) X of X.

(c) Tabulate for X the probability distribution P_x(X = x) for x ∈ X in terms of the success probability p.

(d) Give the cdf F_x of X (Remember that F_x(x) must be defined for all x ∈ R) in terms of the success probability p.

(e) Make an accurate drawing of the cdf F_x of X in the case p = 1/2.

(f) State whether X is a discrete or a continuous rv and why.

Expert Solution

orchestra answered 2 years ago

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