Question

Problem(13) (10 points) An unfair coin is tossed, and it is assumed that the chance of getting a head, H. is (Thus the chance of setting tail, T. is.) Consider a random experiment of throwing the coin 5 times. Let S denote the sample space (a) (2 point) Describe the elements in S. (b) (2 point) Let X be the random variable that corresponds to the number of the heads coming up in the four times of tons. What are the values that the random variable X takes (c) (2 points) Find the probability that there is one tail and three heads, that is, PCX 23). (d) (2 points) Suppose that for each toss that comes up heads we win $3, but for each toss that comes up tails we lose $2. Clearly, a quantity of interest in this situation is our total wining. Let Y denote this quantity. What are the values that the random variable Y takes? (3) (2 points) Find P(Y < 10).

Answer 1

Answer:---- Date:---15/07/2019

given that an unfair coin is tossed, then P(Head) = { and P(Tail) = number of times the experiment conducted, n-4 a)the sample space contains 2* = 16 elements HHHH, HHHT, HHTH ,HTHH,THHH, 7 The sample space,S = HHTT,HTTH,TTHH.HTHT,THHT, THTH,H77T,THTT,77TH,7THT, TTTT let X be the random variable corresponds to the number of heads coming up in the 4 times of tosses of coin then, X may take 0,1,2,3,4 values, that is, number of heads appeared may be 0.1 head, 2 head, 3 head and all heads.

(73) - (13)) .(ج (13 - 2م + (ا=7) + (و=r1- = اری۵۰ (۰) روبا + 4 (0 (4) , ) - = 3 (0 . 4 ربه ..) + و کا0 . 3 + 0 . 34 +54 0 . 87 -( - اک ۱۰ ۔ / : 4 / 4 د.ه - -

Y takes values $12(all 4 heads) and $7 (3heads and 1 tail) $2(2 head and 2 tails),-$3(1 head and 3 tails) -$6 (all 4 tails) the corresponding probabilities are (1/16) and (4/16), (6/16),(4/16), (1/16) P(Y=0)=P(winning $0) P(Y <10)=1 - P(Y>10) = 1 - P(Y=12) -1- 16