There are four cards numbered 1,3,5 and 7, one number on one card Two cards are drawn at random - Maths - Probability

Question

There are four cards numbered 1,3,5 and 7, one number on one card
Two cards are drawn at random without replacement Let X denote the
sum of the numbers on the two drawn cards Find the mean and
variance of X

Anupam Sharma · Accepted Answer

Dear Student,

Numbers on cards=1,3,5,7X=4,6,8,10,12nS=12X=4  when  we get 1,3 or 3,1P(X=4)=212X=6 when we get 1,5 or 5,1P(X=6)=212X=8 when we get 1,7 or 7,1 or 3,5 or 5,3P(X=8)=412X=10 when we have 3,7 or 7,3P(X=10)=212X=12 when we have 5,7 or 7,5P(X=12)=212Mean=∑ipixi=4212+6212+8412+10212+12212=1128+12+32+20+24=9612=8∑ipixi2=16212+36212+64412+100212+144212=11232+72+256+200+288=84812Varience=84812-82=70
666-64=6 666

Regards

There are four cards numbered 1,3,5 and 7, one number on one card. Two cards are drawn at random without replacement. Let X denote the sum of the numbers on the two drawn cards. Find the mean and variance of X.