A continuous RV, x has a cumulative probability distribution function (CDF) defined as follows: Fx(x) =...

    

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A continuous RV, x has a cumulative probability distribution function (CDF) defined as follows: Fx(x) = kx for 0≤x≤a = [k/(b-a)] x[bx-x²/2] for a ≤x≤ b = 1 for x> b where a and bare arbitrary constants. Find the following given that, a = 0.65 and b = 1.75, and k = 0.15. The expected value of the RV Second moment of the RV distribution Standard deviation of the RV distribution Suppose the value of (a = 0.65) represents the median of the RV: x of the CDF indicated. Find the corresponding values of the set. {b, k} PDF, fx(x) of x over the specified range of RV Multiple-choice Answers: Choose the Correct Result ii iii iv V 1 0.1768 0.2011 0.4282 (1.95, 0.716) fx(x) = k for 0 ≤x≤a = [k/(b + a)] x[b-x] for a ≤x≤ b = 0 otherwise 2 0.1678 0.2055 0.4187 (1.89, 0.696) fx(x)= k for 0≤x≤a = [k/(b + a)] x[b+x] for a ≤x≤ b = 0 otherwise 3 0.1878 0.2449 0.4578 (1.95, 0.769) fx(x) = k for 0≤xsa = [k/(ba)] x[b-x] for a ≤x≤ b = 0 otherwise 4 0.1839 0.2045 0.4119 (1.88, 0.714) fx(x)= k for 0 sxsa = [k/(b-a)] x[b-x] for a ≤x≤ b = 0 otherwise 5 0.1798 0.2152 0.4106 (1.93, 0.804) fx(x) = k for 0 ≤x≤a = [k/(b-a)] x[b-x] for a ≤x≤ b = 0 otherwise A continuous RV, x has a cumulative probability distribution function (CDF) defined as follows: Fx(x) = kx for 0≤x≤a = [k/(b-a)] x[bx-x²/2] for a ≤x≤ b = 1 for x> b where a and bare arbitrary constants. Find the following given that, a = 0.65 and b = 1.75, and k = 0.15. The expected value of the RV Second moment of the RV distribution Standard deviation of the RV distribution Suppose the value of (a = 0.65) represents the median of the RV: x of the CDF indicated. Find the corresponding values of the set. {b, k} PDF, fx(x) of x over the specified range of RV Multiple-choice Answers: Choose the Correct Result ii iii iv V 1 0.1768 0.2011 0.4282 (1.95, 0.716) fx(x) = k for 0 ≤x≤a = [k/(b + a)] x[b-x] for a ≤x≤ b = 0 otherwise 2 0.1678 0.2055 0.4187 (1.89, 0.696) fx(x)= k for 0≤x≤a = [k/(b + a)] x[b+x] for a ≤x≤ b = 0 otherwise 3 0.1878 0.2449 0.4578 (1.95, 0.769) fx(x) = k for 0≤xsa = [k/(ba)] x[b-x] for a ≤x≤ b = 0 otherwise 4 0.1839 0.2045 0.4119 (1.88, 0.714) fx(x)= k for 0 sxsa = [k/(b-a)] x[b-x] for a ≤x≤ b = 0 otherwise 5 0.1798 0.2152 0.4106 (1.93, 0.804) fx(x) = k for 0 ≤x≤a = [k/(b-a)] x[b-x] for a ≤x≤ b = 0 otherwise