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Joint Probability Distributions

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Determine the value of c that makes the function f(x,y) = c(x+y) a joint probability density function over the range:
x greater than 0 and less than 3 and x less than y less than x+2

a) P(X<1, Y<2)
b) P(1<X<2)
c) P(Y>1)
d) P(X<2, Y<2)
e) E(X)
f) V(X)
g) Marginal probability distribution of X
h) Conditional probability distribution of Y given that X=1
i) E(Y|X=1)
j) P(Y>2|X=1)

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Normal Distribution and Joint Probability Distribution

54. Suppose the sediment density (g/cm) of a randomly selected specimen from a certain region is normally distributed with mean 2.65 and standard deviation .85 (suggested in "Modeling Sediment and Water Column Interactions for Hydrophobic Pollutants," Water Research, 1984: 1169?1174).

a. If a random sample of 25 specimens is selected, what is the probability what is the probability that the sample average sediment density is at most 3.00? Between 2.65 and 3.00?

b. How large a sample size would be required to ensure the the first probability in part (a) is at least .99?

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