The mean is 7.5 and variance is 3.0625.
The 5 cards are numbered as 1,2,3,4,5. Let S be the sample space and we have 5×4=20 elements in sample space.
Here X is sum of numbers on two drawn cards, X can be 3,4,5,6,7,8,9,10,11,12
P(X=3)=120=120
P(X=4)=120=120
P(X=5)=220=110
P(X=6)=320=320
P(X=7)=320=320
P(X=8)=220=110
P(X=9)=220=110
P(X=10)=120=120
P(X=11)=120=120
P(X=12)=120=120
∑PiXi =
3×120+4×120+5×110+6×320+7×320+8×110+9×110+10×120+11×120+12×12010
=7510
=7.5
∑Pi(Xi−7.5)2×Pi
=1×120×2.25+1×120×2.25+4×110×1.25+9×320×0.25+16×320×0.25+4×110×1.25+4×110×1.25+1×120×2.25+4×120×2.25+4×120×2.2510=30.62510
=3.0625
Question:-
There are 5 cards numbered 1 to 5 , one number on one number on one card . Two cards are drawn at random without replacement . Let X denotes the sum of the numbers on two cards drawn . Find the mean and variance of X.