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- [Q1] The probability distribution of the discrete random variable X is: f(X) = k23-* , for x = 4,5,6, 7 (a) Find: • the value of the constant k. • The mean E(X). • The variance Var(X). (b) Sketch F(X).Prove thisLet X be a uniform random variable over the interval1 to 4 and Y is exponential with a mean of 2. If the correlation between X and Y is 0.5 then compute the covariance between 3X and -5Y i.e. Cov(3X,-5Y)
- Q2. Let X be a random variable with (a) Find E(X) (b) Find M(t). (0.42 f(x)=0.46 0.12 if x = 0 if x = 1 if x = 2Prove the propertyEstablish the following: 0P (E)1 , P (A u B) = P (A) + P (B) – P (A n B) , P (A) = 1 – P (A’) ii The probability that a boy with a catapult hits target A is 2/3and that he hits target B is ¾. Given the probability of hitting both targets to be 1/2, find the probability that he (a) hits at least one of the targets (b) does not hit any. iii What is the probability of having at least one 6 in three throws with a dice?
- Q1 Let probability distribution function of Xbe defined by х %3D 0,1, 2, 3. a P(x) = otherwise. Find the value of a. (а) (b) (c) (d) Find P(-1Type i light bulbs function for a random amount of time having mean µi andstandard deviation σi, i = 1, 2. A light bulb randomly chosen from a bin of bulbs is atype 1 bulb with probability p and type 2 bulb with probability 1 −p. Let X denote thelifetime of this bulb. Find:(a) E(X);(b) Var(X)[Q1] The probability distribution of the discrete random variable X is: f(X) = k23-* , for x = 4,5, 6, 7 (a) Find: • the value of the constant k. • The mean E (X). • The variance Var(X). (b) Sketch F(X).Recommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON