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A person decides to toss a fair coin repeatedly until he gets a head. He will make at most 3 tosses. Let the random variable Y denote the number of heads. The value of var {Y} , where var {.} denotes the variance, equals
  • a)
    7/8
  • b)
    49/64
  • c)
    7/64
  • d)
    105/64
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A person decides to toss a fair coin repeatedly until he gets a head. ...
Solution:
Let's list all the possible outcomes of the experiment.

The possible outcomes of the experiment are:
H, TH, TTH, TTT
where H denotes the event of getting a head on the first toss, TH denotes the event of getting a tail on the first toss and a head on the second toss, and so on.

The corresponding probabilities of the outcomes are:
P(H) = 1/2, P(TH) = (1/2)^2 = 1/4, P(TTH) = (1/2)^3 = 1/8, P(TTT) = (1/2)^3 = 1/8

The expected value of Y is:
E(Y) = 1*P(H) + 2*P(TH) + 3*P(TTH) + 3*P(TTT) = 1/2 + 2/4 + 3/8 + 3/8 = 7/4

The variance of Y is:
Var(Y) = E(Y^2) - [E(Y)]^2

We have:
E(Y^2) = 1^2*P(H) + 2^2*P(TH) + 3^2*P(TTH) + 3^2*P(TTT) = 1/2 + 4/4 + 9/8 + 9/8 = 49/8

Therefore,
Var(Y) = E(Y^2) - [E(Y)]^2 = 49/8 - (7/4)^2 = 7/64

Hence, the correct option is (c) 7/64.
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A person decides to toss a fair coin repeatedly until he gets a head. ...
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A person decides to toss a fair coin repeatedly until he gets a head. He will make at most 3 tosses. Let the random variable Y denote the number of heads. The value of var {Y} , where var {.} denotes the variance, equalsa)7/8b)49/64c)7/64d)105/64Correct answer is option 'C'. Can you explain this answer?
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