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Consider the following probability density function for a continuous random variable. 7 kzz if2 S :1: S 5, f(z) 7 {0 otherwise (a) Determine the value of kfor 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.) 500 = median = (d) Find E(X2), the variance, and the standard deviation. (Round your answers to 4 decimal places, if needed.) E(X2) = V00 = 8000 = Check