z Q(z) z Q(z) 0.0 5.000e-01 3.0 1.350e-03 0.1 4.602e-01 3.1 9.677e-04 0.2 4.207e-01 3.2 6.872e-04...

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z Q(z) z Q(z) 0.0 5.000e-01 3.0 1.350e-03 0.1 4.602e-01 3.1 9.677e-04 0.2 4.207e-01 3.2 6.872e-04 0.3 3.821e-01 3.3 4.835e-04 0.4 3.446e-01 3.4 3.370e-04 0.5 3.085e-01 3.5 2.327e-04 0.6 2.743e-01 3.6 1.591e-04 0.7 2.420e-01 3.7 1.078e-04 0.8 2.119e-01 3.8 7.237e-05 0.9 1.841e-01 3.9 4.812e-05 1.0 1.587e-01 4.0 3.17e-05 1.1 1.357e-01 4.5 3.40e-06 1.2 1.151e-01 5.0 2.87e-07 1.3 9.680e-02 5.5 1.90e-08 1.4 8.076e-02 6.0 9.87e-10 1.5 6.681e-02 6.5 4.02e-11 1.6 5.480e-02 7.0 1.28e-12 1.7 4.457e-02 7.5 3.19e-14 1.8 3.593e-02 8.0 6.22e-16 1.9 2.872e-02 8.5 9.48e-18 2.0 2.275e-02 9.0 1.13e-19 2.1 1.786e-02 9.5 1.05e-21 2.2 1.390e-02 10.0 7.62e-24 2.3 1.072e-02 2.4 8.198e-03 2.5 6.210e-03 2.6 4.661e-03 2.7 3.467e-03 2.8 2.555e-03 2.9 1.866e-03 Consider the following continuous random variables, all of which have mean 46: X is a uniform random variable on the interval 466 Y is an exponential random variable with mean 46 . Z is a Gaussian random variable with mean 46 and variance 16 (a) (6 points.) Compute P(X E [40,50]). (b) (7 points.) Compute P(YE [40,50]). (c) (7 points.) Compute P(ZE [40,50]). z Q(z) z Q(z) 0.0 5.000e-01 3.0 1.350e-03 0.1 4.602e-01 3.1 9.677e-04 0.2 4.207e-01 3.2 6.872e-04 0.3 3.821e-01 3.3 4.835e-04 0.4 3.446e-01 3.4 3.370e-04 0.5 3.085e-01 3.5 2.327e-04 0.6 2.743e-01 3.6 1.591e-04 0.7 2.420e-01 3.7 1.078e-04 0.8 2.119e-01 3.8 7.237e-05 0.9 1.841e-01 3.9 4.812e-05 1.0 1.587e-01 4.0 3.17e-05 1.1 1.357e-01 4.5 3.40e-06 1.2 1.151e-01 5.0 2.87e-07 1.3 9.680e-02 5.5 1.90e-08 1.4 8.076e-02 6.0 9.87e-10 1.5 6.681e-02 6.5 4.02e-11 1.6 5.480e-02 7.0 1.28e-12 1.7 4.457e-02 7.5 3.19e-14 1.8 3.593e-02 8.0 6.22e-16 1.9 2.872e-02 8.5 9.48e-18 2.0 2.275e-02 9.0 1.13e-19 2.1 1.786e-02 9.5 1.05e-21 2.2 1.390e-02 10.0 7.62e-24 2.3 1.072e-02 2.4 8.198e-03 2.5 6.210e-03 2.6 4.661e-03 2.7 3.467e-03 2.8 2.555e-03 2.9 1.866e-03 Consider the following continuous random variables, all of which have mean 46: X is a uniform random variable on the interval 466 Y is an exponential random variable with mean 46 . Z is a Gaussian random variable with mean 46 and variance 16 (a) (6 points.) Compute P(X E [40,50]). (b) (7 points.) Compute P(YE [40,50]). (c) (7 points.) Compute P(ZE [40,50]).