13) Find the mean, variance and skew of the random variable X whose density function is:...

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13) Find the mean, variance and skew of the random variable X whose density function is: Q(z) 0.5 0.80 0.85 Table of Q Function Table 1: Values of Q(z) for 0≤x≤9 Q(z) H Q(G) 5.231x10 6.80 2.1125x10-6 Q(z) 0.010724 4.55 2.6823x10 0.0093867 4.60 0.0081975 4.65 1.6597x10- 0.0071428 4.70 0.0062097 4.75 6.85 3.6925x10-12 6.90 2.6001x10-12 1.3008x10-6 6.96 1.8264x10-12 1.0171x10 7.9333x10-7 4.85 6.1731x10-7 4.90 4.7918x 10-7 7.00 1.2798x10-12 0.0053861 4.80 7.05 8.9459x10-13 0.0046612 7.10 6.2378x10-13 0.0040246 7.15 4.3389x10-13 0.003467 4.95 3.7107x10-7 7.20 3.0106x10-13 0.0029798 5.00 2.8665x10-7 7.25 2.0839x10-13 0.0025551 5.05 2.2091x10-7 7.30 1.4388x10-13 0.002186 5.10 1.6083x10-7 7.35 9.9103x10-14 0.0018658 5.15 1.3024x10-7 7.40 6.8092x10-14 0.0015889 5.20 9.9644x10 7.45 4.667x10-14 0.0013499 5.25 7.605×10- 7.50 3.1909x10-14 0.0011442 5.30 5.7901x10-5 7.55 2.1763x10-14 0.0009676 5.35 4.3977x10-* 7.60 1.4807x10-14 0.00081635 5.40 3.332x10- 7.65 1.0049x10-14 0.00068714 5.45 2.5185x108 7.70 6.8033x 10-15 7.75 4.5946x10-15 0.00057703 5.50 1.899x10 0.00048342 5.55 1.4283x108 7.80 3.0054x10-15 F 0.00 2.30 0.05 0.48006 2.35 0.10 0.46017 2.40 0.15 0.44038 2.45 0.20 0.42074 2.50 0.25 0.40129 2.55 0.30 0.38209 2.60 0.35 0.36317 2.65 0.40 0.34458 2.70 0.45 0.32636 2.75 0.50 0.30854 2.80 0.55 0.29116 2.85 0.60 0.27425 2.90 0.65 0.25785 2.95 0.70 0.24196 3.00 0.75 0.22663 3.05 0.21186 3.10 0.19766 3.15 0.90 0.18406 3.20 0.95 0.17106 3.25 1.00 0.15866 3.30 0.14686 3.35 0.00040406 5.60 1.0718x10 7.85 2.0802x 10-15 1.05 1.10 8.00 0.13567 3.40 0.00033693 5.65 8.0224×109 7.90 1.3945x 10-15 1.15 0.12507 3.45 0.00028029 5.70 5.9904x109 7.96 9.3256x10-16 1.20 0.11507 3.50 0.00023263 5.75 4.4622x10- 6.221x10-16 1.25 0.10565 3.55 0.00019262 5.80 3.3157×109 8.05 4.1397x10-16 1.30 0.0968 3.60 0.00015911 5.85 2.4579x10 8.10 2.748x10-16 1.35 0.088508 3.65 0.00013112 5.90 1.8175x10 8.15 1.8196x10-16 1.40 0.080757 3.70 0.0001078 5.95 1.3407x10-9 8.20 1.2019x10-16 1.45 0.073529 3.75 8.8417x10- 6.00 9.8659x10-10 8.25 7.9197x10-17 1.50 0.066807 3.80 7.2348x10-5 6.05 7.2423x10-10 8.30 5.2056x 10-17 1.55 0.060571 3.85 5.9059x105 6.10 5.3034x10-10 8.35 3.4131x10-17 1.60 0.054799 3.90 4.8096x10-5 6.15 3.8741x10-10 8.40 2.2324x10-17 1.65 0.049471 3.95 3.9076x10-5 6.20 2.8232x10-10 8.45 1.4565x10-17 1.70 0.044565 4.00 3.1671x10 6.25 2.0523x10-10 8.50 9.4795x10-18 1.75 0.040059 4.05 2.5609x10- 6.30 14882x10-10 8.55 6.1544x10-18 1.80 0.03593 4.10 2.0658x10-5 6.35 1.0766x10-10 8.60 3.9858x10-18 1.85 0.032157 4.15 1.6624x10-5 6.40 7.7688x10-11 8.65 2.575x10-18 1.90 0.028717 4.20 1.3346x10 6.45 5.5925x10-11 8.70 1.6594x 10-18 1.95 0.025588 4.25 1.0689x105 6.50 4.016x10-11 8.75 1.0668x10-18 2.00 0.02275 4.30 8.5399x10 6.55 2.8769x10-11 8.80 6.8408x10-19 2.05 0.020182 4.35 6.8069x10-6 6.60 2.0558x10-11 8.85 4.376x10-19 2.10 0.017864 4.40 5.4125x10 6.65 1.4655x10-11 8.90 2.7923x10-19 2.15 0.015778 4.45 4.2935x10 6.70 1.0421x10-11 8.95 1.7774x10-19 2.20 0.013903 4.50 3.3977x10 6.75 7.3923x10-12 9.00 1.1286x10-19 2.25 0.012224 13) Find the mean, variance and skew of the random variable X whose density function is: Q(z) 0.5 0.80 0.85 Table of Q Function Table 1: Values of Q(z) for 0≤x≤9 Q(z) H Q(G) 5.231x10 6.80 2.1125x10-6 Q(z) 0.010724 4.55 2.6823x10 0.0093867 4.60 0.0081975 4.65 1.6597x10- 0.0071428 4.70 0.0062097 4.75 6.85 3.6925x10-12 6.90 2.6001x10-12 1.3008x10-6 6.96 1.8264x10-12 1.0171x10 7.9333x10-7 4.85 6.1731x10-7 4.90 4.7918x 10-7 7.00 1.2798x10-12 0.0053861 4.80 7.05 8.9459x10-13 0.0046612 7.10 6.2378x10-13 0.0040246 7.15 4.3389x10-13 0.003467 4.95 3.7107x10-7 7.20 3.0106x10-13 0.0029798 5.00 2.8665x10-7 7.25 2.0839x10-13 0.0025551 5.05 2.2091x10-7 7.30 1.4388x10-13 0.002186 5.10 1.6083x10-7 7.35 9.9103x10-14 0.0018658 5.15 1.3024x10-7 7.40 6.8092x10-14 0.0015889 5.20 9.9644x10 7.45 4.667x10-14 0.0013499 5.25 7.605×10- 7.50 3.1909x10-14 0.0011442 5.30 5.7901x10-5 7.55 2.1763x10-14 0.0009676 5.35 4.3977x10-* 7.60 1.4807x10-14 0.00081635 5.40 3.332x10- 7.65 1.0049x10-14 0.00068714 5.45 2.5185x108 7.70 6.8033x 10-15 7.75 4.5946x10-15 0.00057703 5.50 1.899x10 0.00048342 5.55 1.4283x108 7.80 3.0054x10-15 F 0.00 2.30 0.05 0.48006 2.35 0.10 0.46017 2.40 0.15 0.44038 2.45 0.20 0.42074 2.50 0.25 0.40129 2.55 0.30 0.38209 2.60 0.35 0.36317 2.65 0.40 0.34458 2.70 0.45 0.32636 2.75 0.50 0.30854 2.80 0.55 0.29116 2.85 0.60 0.27425 2.90 0.65 0.25785 2.95 0.70 0.24196 3.00 0.75 0.22663 3.05 0.21186 3.10 0.19766 3.15 0.90 0.18406 3.20 0.95 0.17106 3.25 1.00 0.15866 3.30 0.14686 3.35 0.00040406 5.60 1.0718x10 7.85 2.0802x 10-15 1.05 1.10 8.00 0.13567 3.40 0.00033693 5.65 8.0224×109 7.90 1.3945x 10-15 1.15 0.12507 3.45 0.00028029 5.70 5.9904x109 7.96 9.3256x10-16 1.20 0.11507 3.50 0.00023263 5.75 4.4622x10- 6.221x10-16 1.25 0.10565 3.55 0.00019262 5.80 3.3157×109 8.05 4.1397x10-16 1.30 0.0968 3.60 0.00015911 5.85 2.4579x10 8.10 2.748x10-16 1.35 0.088508 3.65 0.00013112 5.90 1.8175x10 8.15 1.8196x10-16 1.40 0.080757 3.70 0.0001078 5.95 1.3407x10-9 8.20 1.2019x10-16 1.45 0.073529 3.75 8.8417x10- 6.00 9.8659x10-10 8.25 7.9197x10-17 1.50 0.066807 3.80 7.2348x10-5 6.05 7.2423x10-10 8.30 5.2056x 10-17 1.55 0.060571 3.85 5.9059x105 6.10 5.3034x10-10 8.35 3.4131x10-17 1.60 0.054799 3.90 4.8096x10-5 6.15 3.8741x10-10 8.40 2.2324x10-17 1.65 0.049471 3.95 3.9076x10-5 6.20 2.8232x10-10 8.45 1.4565x10-17 1.70 0.044565 4.00 3.1671x10 6.25 2.0523x10-10 8.50 9.4795x10-18 1.75 0.040059 4.05 2.5609x10- 6.30 14882x10-10 8.55 6.1544x10-18 1.80 0.03593 4.10 2.0658x10-5 6.35 1.0766x10-10 8.60 3.9858x10-18 1.85 0.032157 4.15 1.6624x10-5 6.40 7.7688x10-11 8.65 2.575x10-18 1.90 0.028717 4.20 1.3346x10 6.45 5.5925x10-11 8.70 1.6594x 10-18 1.95 0.025588 4.25 1.0689x105 6.50 4.016x10-11 8.75 1.0668x10-18 2.00 0.02275 4.30 8.5399x10 6.55 2.8769x10-11 8.80 6.8408x10-19 2.05 0.020182 4.35 6.8069x10-6 6.60 2.0558x10-11 8.85 4.376x10-19 2.10 0.017864 4.40 5.4125x10 6.65 1.4655x10-11 8.90 2.7923x10-19 2.15 0.015778 4.45 4.2935x10 6.70 1.0421x10-11 8.95 1.7774x10-19 2.20 0.013903 4.50 3.3977x10 6.75 7.3923x10-12 9.00 1.1286x10-19 2.25 0.012224