examples for general continuous%2c uniform%2c and exponential distributions

Examples for general continuous%2c uniform%2c and exponential distributions

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1. f[x]=3x^2 2x + 2 for the interval .5< x < c. a) Find c that makes f[x] legitimate. b) Find F[x]. c) Find the probability that X is more than .75. d) Find the probability that X is less than .6. e) Find E[X]. f) Find E[X^2] and then Var(X). Let F[X] = 4x^3 - 12x^2 + 4x 2 from 2.69804806238812 < X < 2.73461011337304 g) Find f[X]. 2. Let X~U(2,7) a) Find the probability that X is between 3 and 5. b) Find the probability that X is at most 4. c) Find the probability that X is at least 3. d) Find E[X]. e) Find the probability that X is at least 4.5. f) Find Var(X). g) Let Y~U(5,10). Find Var(Y). Does this answer surprise you? 3. Let T~Expo(lambda=5) a) Find the probability that T is more than 4. b) Find the probability that T is at most 2.5. c) Find the probability that T is less than 1 but more than .2. d) Find E[X]. e) Find Var(X).
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(Do a change of time unit problem) 4. Suppose S~ Exponential with a mean of 5 minutes. a) What is lambda?
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Examples for general continuous%2c uniform%2c and exponential distributions

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