S1 Basic Test II 1. Consider the probability distribution x P(X = x)
(a) By considering the p
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S1 Test I 1. If X ∼ B(25, 0.4) calculate: (a) P(X = 12),
(b) P(X > 14).
2. If Y ∼ Geo( 14 ) calculate: (a) P(Y = 4),
(b) P(Y 6 8).
3. X is a discrete random variable: 1 2k
x P(X = x)
(a) Find the value of k.
(b) Find E(X).
(c) Find Var(X).
4. On my way to work I pass nine traffic lights. The probability any one is green when I arrive is 0.7. The signal at one light is independent of the others. Calculate the probability: (a) all the lights are green.
(b) exactly five are green.
(c) at least six are green.
5. Two variables are measured as shown in the table. x 2 4 6 8 10
y 19 16 15 13 10
(a) Calculate the correlation coefficient r. (b) Comment on your result.
−0.9878 Strong negative correlation
6. A normal six sided die is thrown until it shows a one, two or a three. Calculate the probability of: (a) Success on the second throw.
(b) At least 5 throws being needed.
(c) Fewer than seven throws required.
7. Two dice are rolled and the square of the difference (always zero or a positive number) of the two scores is recorded. (a) Tabulate the possible scores with their probabilities. (b) Calculate the expectation of D.