[June 2009 Q6] 5. The three independent random variables and each has a continuous uniform A, B C distribution over the interval [0, 5]. (a) Find P(A > 3). (1) (b) Find the probability that and are all greater than 3. (2) A, B C The random variable represents the maximum value of and Y A, B C. The cumulative distribution function of is Y F(y) = (c) Find the probability density function of (2) Y. (d) Sketch the probability density function of (2) Y. (e) Write down the mode of (1) Y. (f) Find E(Y). (3) (g) Find P(Y > 3). (2) [Jan 2009 Q2] 6. The continuous random variable is uniformly distributed over the interval [–2, 7]. X (a) Write down fully the probability density function f(x) of (2) X. (b) Sketch the probability density function f(x) of (2) X. Find (c) E(X 2), (3) (d) P(– 0.2 < < 0.6). (2) X [June 2009 Q6] 5. The three independent random variables and each has a continuous uniform A, B C distribution over the interval [0, 5]. (a) Find P(A > 3). (1) (b) Find the probability that and are all greater than 3. (2) A, B C The random variable represents the maximum of and Y A, B C. The cumulative distribution function of is Y F(y) = (c) Find the probability density function of (2) Y. (d) Sketch the probability density function of (2) Y. (e) Write down the mode of (1) Y. (f) Find E(Y). (3) (g) Find P(Y > 3). (2) [Jan 2009 Q2] 6. The continuous random variable is uniformly distributed over the interval [–2, 7]. X (a) Write down fully the probability density function f(x) of (2) X. (b) Sketch the probability density function f(x) of (2) X. Find
[June 2009 Q6] 5. The three independent random variables A, B and C each has a continuous uniform distribution over the interval [0, 5]. (a) Find P(A > 3). (1) (b) Find the probability that A, B and C are all greater than 3. (2) The random variable Y represents the maximum value of A, B and C. The cumulative distribution function of Y is F(y) = (c) Find the probability density function of Y. (2) (d) Sketch the probability density function of Y. (2) (e) Write down the mode of Y. (1) (f) Find E(Y). (3) (g) Find P(Y > 3). (2) [Jan 2009 Q2] 6. The continuous random variable X is uniformly distributed over the interval [–2, 7]. (a) Write down fully the probability density function f(x) of X. (2) (b) Sketch the probability density function f(x) of X. (2) Find (c) E(X 2), (3) (d) P(– 0.2 < X < 0.6). (2) [June 2009 Q6] 5. The three independent random variables A, B and C each has a continuous uniform distribution over the interval [0, 5]. (a) Find P(A > 3). (1) (b) Find the probability that A, B and C are all greater than 3. (2) The random variable Y represents the maximum of A, B and C. The cumulative distribution function of Y is F(y) = (c) Find the probability density function of Y. (2) (d) Sketch the probability density function of Y. (2) (e) Write down the mode of Y. (1) (f) Find E(Y). (3) (g) Find P(Y > 3). (2) [Jan 2009 Q2] 6. The continuous random variable X is uniformly distributed over the interval [–2, 7]. (a) Write down fully the probability density function f(x) of X. (2) (b) Sketch the probability density function f(x) of X. (2) Find
S2-Chp4-ContinuousUniformDistrib-ExamQuestionsWithSolutions.docx