Question

an urn contains 5 balls numbered 1 to 5. two balls are selected at random without replacement from the urn. if the random variable X denotes the sum of the numbers on the 2 balls, then what are the space and the probability density function of X?​

Answer 1

Answer:

We have 5 choices to select two numbers. So there are 5C2 = 10 choices. So sample space = (1,2),(1,3), (1,4), (1,5),(2,3), (2, 4), (2,5), (3,4),(3,5),(4,5) a) The largest of two sampled numbers are either 2, 3, 4 or 5 To get answer 2, probability is 1 / 10 To get answer 3, probability is 2 / 10 = 1/5 To get answer 4, probability is 3/10 To get answer 5, probability is 4/10 = 2/5 This is the required probability distribution. b) In this part we need sum. The choices for sums are 3 , 4, 5, 6, 7 , 8, 9 To get sum 3 it may be from pair (1,2) only. So probability is 1/10 To get sum 4 there is only one choice (1,3) So probability is 1/10...