(a) If the joint probability distribution of X and Y is givenby f(x,y)=(x+y)/30

Question

(a) If the joint probability distribution of X and Y is givenby
f(x,y)=(x+y)/30 for x = 0,1,2.3 and y=0,1,2

Find
1. P(X<=2, Y=1)
2. P(X+Y=4)

(b) An electrical firm manufactures light bulbs that have a lengthof life that is normally distributed with mean equal to 800 hoursand a standard deviation of 40 hours. Find the probability that abulb burns
(i) Less than 778 hours.
(ii) Between 778 and 834 hours.
Question 2 20 Marks
(a) The average number of days school is closed due to snow duringthe winter in a certain city in the eastern part of United Statesis 4.What is the probability that the school in this city willclose for 2 or more days during winter?
(b) Is there any inconsistency in the statement that the mean of abinomial distribution is 20 and its standard deviation is 4? If noinconsistency is found what shall be the values of p, q and n.

Explanation / Answer

I have solved this at different types of probabilitydistributions.

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