You have an unfair coin: the probability that it comes up heads on a single toss is 0.3. You offer to play a game with a friend. If it comes up heads twice in a row, you give them $1. If it doesn't, they give you $4. What are your expected winnings in this game? (Remember that winnings can be positive or negative!)

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You have an unfair coin: the probability that it comes up heads on a single toss is 0.3. You offer to play a game with a friend. If it comes up heads twice in a row, you give them $1. If it doesn&#039;t, they give you $4. What are your expected winnings in this game? (Remember that winnings can be positive or negative!)

Edward Belanger · Accepted Answer

Step 1  Random variables are of 2 types, discrete and continuous. A discrete random variable can only take countable and finite number of possible values.  A continuous random variable can take infinitely and uncountably many possible values. Expectation of a random variable is same as the mean of the random variable. Probability distributions are also of two types based on the classification of random variables, discrete and continuous distributions  Step 2  It is given that the probability of getting a head is 0.3. So the probability of getting 2 heads in a row will be 0.3⋅0.3=0.09. When 2 heads comes up the player give $1. Probability of not getting 2 heads in a row is 1−0.09=0.91 (since the sum of probabilities is 1). When this happen the player receives $4. So the probability distribution is given below.  Winning(W)−14Probability0.090.91  The expected winning can be calculated in the following way.  E(W)=∑i=1nWi⋅P(Wi)  =(−1⋅0.09)+(4⋅0.91)  =−0.09+3.64  =3.55  So the expected winning is $3.55.

You have an unfair coin: the probability that it comes up heads on a s

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