Let X be an exponential random variable with parameter whose pdf is b e-a X 0...

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Let X be an exponential random variable with parameter whose pdf is b e-a X 0 f(x) = { 0, elsewhere (amo). The graph below represents the probability density function associated with the function. a. Find the value of graphically. Sovive 2 ytor doug srb at redw b. Using the value from question a, Calculate P (X < 1) and P (X 2). c. Find the expectation E(X) and Var().a teor and b bam lemonid och to be a boil 9 (asain) yd navige motout ob pilidadong saodw sideitsy mobum euongiosa ai Xd secqqu? 1 >>0 STS/wals 0 1 23 am 4th) arba D 18 level a tood withab avitelum di (x) A bit d Suppose that X is a continuous random variable whose probability density function is given by {C2x+1, 0 < x <1 f(x) = {C2x elswhere a. Evaluate c that renders f(x) a valid density function. b. Find F (x) the cumulative density function (CDF). C. Evaluate P (0.3 < x < 0.6) using the CDF. d. Find the expectation EX] and Var(X) of the random variable X. Let X be an exponential random variable with parameter whose pdf is b e-a X 0 f(x) = { 0, elsewhere (amo). The graph below represents the probability density function associated with the function. a. Find the value of graphically. Sovive 2 ytor doug srb at redw b. Using the value from question a, Calculate P (X < 1) and P (X 2). c. Find the expectation E(X) and Var().a teor and b bam lemonid och to be a boil 9 (asain) yd navige motout ob pilidadong saodw sideitsy mobum euongiosa ai Xd secqqu? 1 >>0 STS/wals 0 1 23 am 4th) arba D 18 level a tood withab avitelum di (x) A bit d Suppose that X is a continuous random variable whose probability density function is given by {C2x+1, 0 < x <1 f(x) = {C2x elswhere a. Evaluate c that renders f(x) a valid density function. b. Find F (x) the cumulative density function (CDF). C. Evaluate P (0.3 < x < 0.6) using the CDF. d. Find the expectation EX] and Var(X) of the random variable X.