a) P(1) = P(2) = P(3) = P(4) = 1/4
1) P(X = 3) = 1/4 = 0.25
2) P(X < 3) = P(X = 1) + P(X = 2) + P(X = 3) = 1/4 + 1/4 + 1/4 = 3/4 = 0.75
3) P(X > 3) = 1 - P(X < 3) = 1 - 0.75 = 0.25
4) P(2 < X < 4) = P(X = 2) + P(X = 3) = 1/4 + 1/4 = 1/2 = 0.5
b) P(Y = y) = 10Cy * 0.5y * (1 - 0.5)10-y
1) P(Y = 3) = 10C3 * 0.53 * 0.57 = 0.1172
2) P(Y < 3) = P(Y = 0) + P(Y = 1) + P(Y = 2) + P(Y = 3)
= 10C0 * 0.50 * 0.510 + 10C1 * 0.51 * 0.59 + 10C2 * 0.52 * 0.58 + 10C3 * 0.53 * 0.57
= 0.1719
3) P(Y > 3) = 1 - P(Y < 3) = 1 - 0.1719 = 0.8281
4) Mean = n * p = 10 * 0.5 = 5
5) Variance = n * p * (1 - p) = 10 * 0.5 * 0.5 = 2.5
6) Standard deviation = sqrt(variance) = sqrt(2.5) = 1.5811
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