1. Suppose X ~ Bin(4, 0.5). The probability mass function (pmf) and cumulative distri- bution function...

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1. Suppose X ~ Bin(4, 0.5). The probability mass function (pmf) and cumulative distri- bution function (cdf) of X are shown in Figure 1. 8 8 - 00 0 PMF of Bin(4, 0.5) F(x) 0.6 0.8 1.0 2 00 CDF of Bin(4, 0.5) 0 3 4 5 Figure 1: Pmf and cdf of Bin(4,0.5). (a) Find the pmf of X first by hand and then using R. That is, find the probabilities f(x) = P(X = x), x = = 0, 1, 2, 3, 4. (b) Find the cdf of X first by hand and then using R. That is, find the probabilities F(x) = P(X x) when (i) x < 0, (ii) 0 1. Suppose X ~ Bin(4, 0.5). The probability mass function (pmf) and cumulative distri- bution function (cdf) of X are shown in Figure 1. 8 8 - 00 0 PMF of Bin(4, 0.5) F(x) 0.6 0.8 1.0 2 00 CDF of Bin(4, 0.5) 0 3 4 5 Figure 1: Pmf and cdf of Bin(4,0.5). (a) Find the pmf of X first by hand and then using R. That is, find the probabilities f(x) = P(X = x), x = = 0, 1, 2, 3, 4. (b) Find the cdf of X first by hand and then using R. That is, find the probabilities F(x) = P(X x) when (i) x < 0, (ii) 0