Question 4 a) A bowl contains six white chips, three red chips and one blue chip. A chip is taken at random from the bowl. Let the random variable X = 1 if a white chip is chosen, let X = 5 if a red chip is chosen and let X = 10 if a blue chip is chosen. Find: i) The probability function f(x) of X. ii) The distribution function F(x) of X. iii) E(X). iv) E(3X² + 5). v) Var(X)

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Chapter1: Combinatorial Analysis
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Question 4
a) A bowl contains six white chips, three red chips and one blue chip. A chip is taken at
random from the bowl. Let the random variable X = 1 if a white chip is chosen, let
X = 5 if a red chip is chosen and let X = 10 if a blue chip is chosen. Find:
i) The probability function f (x) of X.
ii) The distribution function F(x) of X.
iii) E(X).
iv) E(3X² + 5).
v) Var(X)
b) A discrete random variable X has probability function f (x) = k(x + 1)²,x = 0,1,2.
i) Find the value of k.
ii) Find E (5X + 3), E (X²) and Var(3X – 2).
c) The discrete random variable X represents the number of days spent by a certain
5-х
patient in a hospital. The probability function of X is f(x) :
-,x = 1,2,3,4. The
10
patient receives $200 from an insurance company for each of the first two days in
hospital, and $100 for each day after the first two days. What is the expected amount
received?
Transcribed Image Text:Question 4 a) A bowl contains six white chips, three red chips and one blue chip. A chip is taken at random from the bowl. Let the random variable X = 1 if a white chip is chosen, let X = 5 if a red chip is chosen and let X = 10 if a blue chip is chosen. Find: i) The probability function f (x) of X. ii) The distribution function F(x) of X. iii) E(X). iv) E(3X² + 5). v) Var(X) b) A discrete random variable X has probability function f (x) = k(x + 1)²,x = 0,1,2. i) Find the value of k. ii) Find E (5X + 3), E (X²) and Var(3X – 2). c) The discrete random variable X represents the number of days spent by a certain 5-х patient in a hospital. The probability function of X is f(x) : -,x = 1,2,3,4. The 10 patient receives $200 from an insurance company for each of the first two days in hospital, and $100 for each day after the first two days. What is the expected amount received?
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