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You draw a card from a deck. If you get a diamond, you win nothing. You lose $2 if getting a heart. If you got a spade, you win $6. For any club, you win $10 plus an extra $5 for the face card of clubs. Define random variable X as the amount you win at one game. What is the pmf of X

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Answer:

Step-by-step explanation:

Let  X = amount you can win at this game (# of dollars you can win)

x = (0, -2, 6, 10, 15)

  • P(X=0) = P(probability of picking a diamond) = 13/52 = .25
  • P(X=-2) = P(probability of picking a heart) = 13/52 = .25
  • P (X= 6) = P(probability of picking a spade) = 13/52 = .25
  • P(X=10) = P(probability of picking a club) = 12/52 ≈ .231
  • P(X=20) = P(probability of picking the ace of clubs) = 1/52 ≈ .019

Probability Distribution of X

x p(X = x) Decimal

0 13/52 0.25

-2 13/52 0.25

6      13/52       0.25

10 12/52 0.231

15 1/52         0.019

Total  52/52   1.00

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