# IMG20230820162359731

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\""'/"n,) '.,k . -1 f't""("') ,['.( les & Binomial DIStribution Revisiopsss »*Discrete Random Variab Make sure you show all steps of working when doing these questions. \ﬂ Find the value of a for l_hcrIbl»lfn}fggrw}_\hnhumy distribution: ) e L } e P - qu'wj,'mn __lej:fQ,- _03 _\ Hence find Pr (X<2)and E(X). @ A random \'arinlllq__\_'j)_-_%_!l\'c_ probability di striby \ random X == } a tion: 4 PrOX=x) 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 Yis such that its mean is 10 and its standard deviation is 5. Find E(X")- Ls A discrete random variable = (& A game is Plﬂ)'cfi by selecting coloured cubes from a box. The box initially contains three red and seven b_\uc cubes. Mr Cashino pays \$10,00 each time he selects tWo cubes. If he gets two red cubes, he gets \$20 prize or loss? Is this a fair game? I not, and if he gets one red cube, he gets a \$10 prize. What is his expected gain what should Mr Cashino be charged to play the game? t a funfair. Xhas a probability distribution as LS) A random variable X represents the points scored on a spinner & shown below: - i 2 A It is known that Var (X) is equal to 6.6. Find: - (@) aandb (b) E(GX-2) (c) Var(3X —2) s the probability that they score at least 5 points exactly twice? A person spins the spinner 5 times. What i d dice are rolled and the sum of the two dice is noted. If the two dice are rolled ten times, what is ecimal places) exactly three times? ss than 5 times? d dice are rolled ten times. If the sum of 7is is obtained no less than 5 times, the playe @ Two coloure the probability (correct todd (2) that the sum of the two dice is 7 (b) that the sum of the two dice is 7 no le <~' b ) A game is played where these two coloure times, the player wins \$5, and if the sum of 7 they have to pay an amount \$C. (). IfGisthe gain obtained by the player playing this game, much C is for the game to be a fair game. obtained exactly three r wins \$10. Otherwise, construct a probability distribution table for G. (d) Hence calculate how
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