1. Consider a random variable X that has probability mass function (pmf) given by X P(X=x)...

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1. Consider a random variable X that has probability mass function (pmf) given by X P(X=x) -2 6 7 8 (a) What is P(X= 6)? (b) What is P(X ≤7)? (c) Find E(X) (the population mean). (d) Find Var(X) (the population variance). 2. Consider a continuous random variable Y with probability density function (pdf) given by f(y) 0.2 0.3 0.35 0.15 (b) Find P(Y<a+b). (c) Find P(c≤ Y≤d), for a <c<d<b. (d) Find E(Y). b-a' a<y<b otherwise This is called the continuous uniform distribution on the interval (a, b), a <b. (a) Sketch the pdf and show that this is a true pdf by verifying that it integrates to 1 over the interval (a, b).. 1. Consider a random variable X that has probability mass function (pmf) given by X P(X=x) -2 6 7 8 (a) What is P(X= 6)? (b) What is P(X ≤7)? (c) Find E(X) (the population mean). (d) Find Var(X) (the population variance). 2. Consider a continuous random variable Y with probability density function (pdf) given by f(y) 0.2 0.3 0.35 0.15 (b) Find P(Y<a+b). (c) Find P(c≤ Y≤d), for a <c<d<b. (d) Find E(Y). b-a' a<y<b otherwise This is called the continuous uniform distribution on the interval (a, b), a <b. (a) Sketch the pdf and show that this is a true pdf by verifying that it integrates to 1 over the interval (a, b)..

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