Discrete random variable X is described by the PMF {K Px (x) - -2, if x...

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Discrete random variable X is described by the PMF {K Px (x) - -2, if x = 0, 1, 2 for all other values of r Let D₁, D2,.. , DN represent N successive independent experimental values of random vari- able X. 1. Determine the numberical value of K. 2. Determine the probability that D₁ > D₂. 3. Determine the probability that D₁ + D₂ + + DN ≤ 1.0 4. Define R= max(D₁, D₂) and S = min(D₁, D₂). Determine the following PMF's for all values of their arguments: (a) ps(s) (b) PRIS (0) (c) PR,S(r, s) (d) Pr(t) with T = (1 + D₁)/(1+S) 5. Determine the expected value and variance of random variable S defined above. 6. Given D₁ + D₂ ≤ 2.0, determine the conditional expected value and conditional variance of random variable S defined above. Discrete random variable X is described by the PMF {K Px (x) - -2, if x = 0, 1, 2 for all other values of r Let D₁, D2,.. , DN represent N successive independent experimental values of random vari- able X. 1. Determine the numberical value of K. 2. Determine the probability that D₁ > D₂. 3. Determine the probability that D₁ + D₂ + + DN ≤ 1.0 4. Define R= max(D₁, D₂) and S = min(D₁, D₂). Determine the following PMF's for all values of their arguments: (a) ps(s) (b) PRIS (0) (c) PR,S(r, s) (d) Pr(t) with T = (1 + D₁)/(1+S) 5. Determine the expected value and variance of random variable S defined above. 6. Given D₁ + D₂ ≤ 2.0, determine the conditional expected value and conditional variance of random variable S defined above.