The lifetime in hours of electronic tubes is random variable having probability distribution function

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

1. An Urn contains 4 tickets numbered 1,2,3,4 and another contains 6 tickets numbered 2,4,6,7,8,9. If one the two urns is chosen at random and a ticket is drawn at random from the chosen urn, find the probabilities that the tickets drawn bears the numbers 2 or 4 (ii) 3 (iii) 1 or 9

2. X and Y are two random variables having the joint density function 𝑓(𝑥, 𝑦) = 2𝑥+𝑦 27 where x and y can assume only the integer values 0,1,2. Find the conditional distribution of Y for X=x.

3. Let S be a sample space and A, B are two mutually exclusive events such that 𝐴 ∪ 𝐵 = 𝑆. Then find the maximum value of 𝑃(𝐴)𝑃(𝐵).

4. The lifetime in hours of electronic tubes is random variable having probability distribution function 𝑓(𝑥) = 𝑎2𝑥𝑒−𝑎𝑥, 𝑥 > 0. Compute expected mean life time of such a tube.

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