Question

2. Suppose 4 Bernoulli trials, each with success probability p, are con ducted such that the outcomes of the 4 experiments pendent. Let the random variable X be the total number of successes over the 4 Bernoulli trials are mutually inde- (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) AX of X (c) Tabulate for X the probability distribution Px(X = x) for x E X in terms of the success probability p. (d) Give the cdf Fx of X (Remember that Fx(x) must be defined for all E R) in terms of the success probability p. (e) Make an accurate drawing of the cdf Fx of X in the case p = 1/2. (f) State whether X is a discrete or a continuous rv and why.

Answer 1

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