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-3 1 I(f"lt) ',-';\f " sDjscrete Random Variables & Binomial Distribution Reyisjopss Make sure you show all steps of working when doing these questions \_D Find the value of a for the following probability distribution: s 0 | e i). | 2a - da Hence find Pr(X'< 2) and E(X). able X has the probability distribution: 2 A random vari X D Find: () the constant k (b) the most likely value of X (a) E(X), the expectation of X' (b) Var(X), the variance of X A discrete random variable X is such that its mean is 10 and its standard deviation is 5. Find E(X . )- tially contains three red and seven blue gets two red cubes, he gets a $20 prize s? Is this a fair game? If not, A game is played by selecting coloured cubes from a box. The box ini cubes. Mr Cashino pays $10.00 each time he selects two cubes. If he and if he gets one red cube, he gets a $10 prize. What is his expected gain or los what should Mr Cashino be charged to play the game? A random variable X represents the points scored on a spinner at a funfair. X has a probability distribution as shown below: x 2 3 ;' a Pr(X =x) 0.2 It is known that Var (X) is equal to 6.6. Find: aand b EGX-2) Var(3X —2) A person spins the spinner 5 times. What is the probability that they score at least 5 points exactly twice? Two coloured dice are rolled and the sum of the two dice is noted. If the two dice are rolled ten times, what is the probability (correct 10 4 decimal places) that the sum of the two dice is 7 exactly three times? that the sum of the two dice is 7 no less than 5 times? A game is played where these two coloured dice are rolled ten times. If the sum of 7 is obtained exactly three times, the player wins $5, and if the sum of 7 is obtained no less than 5 times, the player wins $10. Otherwise, they have to pay an amount $C. If G is the gain obtained by the player playing th Hence calculate how much C is for the game to be a fair game. is game, construct a probability distribution table for G.
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