4. A bag contains 5 coins, one of which has a head on both sides while the other

Question

4. A bag contains 5 coins, one of which has a head on both sides while the other 4 coins are normal. A coin is chosen at random from the bag and tossed 2 times. The number of heads obtained is a random variable, say X. (a) What are the possible values of X? Also tabulate the pmf of X. (Hint: The coin chosen is either normal or with head on both sides. Find the conditional probability of X for each of these two situations. Then use the law of total probability and multiplication rule to find the probability of x.) (b) Calculate E(X) and Var(x).

Explanation / Answer

a)as out of 2 trails there can be 0,1,2 heads hence

here possible values of X are = {0,1,2}

below is pmf of X:

P(X=0)=P(failr coin and 0 heads)+P(unfair coin and 0 heads) =(4/5)*(1/2)*(1/2)+(1/5)*(0)=1/5 =0.2

P(X=1)=P(failr coin and 1 heads)+P(unfair coin and 1 heads) =(4/5)*(1/2)+(1/5)*0 =2/5 =0.4

P(X=2)=P(failr coin and 2 heads)+P(unfair coin and 2 heads) =(4/5)*(1/2)*(1/2)+(1/5)*1=2/5 =0.4

b)

from above E(X) =1.2 and Var(X) =0.56

x P(x) xP(x) x2P(x) 0 0.2000 0.0000 0.0000 1 0.4000 0.4000 0.4000 2 0.4000 0.8000 1.6000 total 1.2 2 E(X) = ?xP(x) = 1.20 E(X2) = ?x2P(x) = 2.00 Var(X)=?2 E(X2)-(E(X))2= 0.560

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.