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Consider the following probability density function for a continuous random variable. _ km'z if23z35, x) _ { 0 otherwise (a) Determine the value of k for which f(x) is a legitimate pdf. Please enter your answer as a fraction (for example, 5/21), without rounding. (b) Find the following probabilities. (Round your answers to 4 decimal places. if needed.) P(X 35) : (c) Find the expected value and median. (Round your answers to 4 decimal places, if needed.) E(X) = median = (d) Find E(X2), the variance, and the standard deviation. (Round your answers to 4 decimal places, if needed.) 50(2) = V(X) = 8000 =