A box contains 10 cards numbered 1 through 10. A card is picked at random from the box. LetXdenote the number on the card. Then another card, from the remaining 9 cards, ispicked at random from the box. LetYdenote the number on the second card. What isE[X−Y]? Explain your answer.

Step-by-step explanation:

Given: Number of cards a box contains = 10 (numbered 1 through 10).

A random card is picked at first instance and is denoted X and then another card is picked from remaining cards and is denoted as Y

Here E(X) = (1+2+3+4+5+6+7+8+9+10)/10 = 5.5

E(Y)=P(X=1) *E(Y|X=1) +P(X=2) *E(Y|X=2) +. .+P(X=10)*E(Y|X=10)

= (1/10) *(2+3+4+ .+10)/9+(1/10)*(1+3+4+..+10)/9++(1/10)*(1+2+3+4+5...+9)/9

= (1/10) *(9/9) *(1+2+3+4+5+6+7+8+9+10) = 5.5

Hence, E(X-Y) = E(X) - E(Y) = 0.000

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