Probability (Class 12) · Question 6

Let X be a random variable, and let P(X=x) denote the probability that X takes the value x. Suppose that the points (x,P(X=x) ), x=0,1,2,3,4, lie on a fixed straight line in the xy-plane, and P(X=x)=0 for all x R-\0,1,2,3,4\. If the mean of X is 52, and the variance of X is , then the value of 24 is .

Answer

42

Solution

Let P(X=x)=mx+c, x=0,1,2,3,4.

P=10m+5c=1 and xP=30m+10c= 52

m= 120, c= 110: probabilities 0.10, 0.15, 0.20, 0.25, 0.30

E(X2)=0+0.15+0.8+2.25+4.8=8

=8- 254= 74 24 =42

Answer: 42