let x be a gaussian random variable with mean m 4 and variance 2 16 ie x n 4 16 compute the foll

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Let X be a Gaussian random variable with mean μ = -4 and variance σ^2 = 16, i.e., X ~ N(-4, 16). Compute the following probabilities (give numerical answers): (a) (1 Point) P[X > 4]. (b) (1 Point) P[|X| < 4]. (c) (2 Points) P[X > -4|X < 4]. (d) (1 Point) P[X < 4|X > -4]. (e) (1 Point) P[X > 4|X > -4]. (f) (1 Point) If P[X < a] = 0.8869, find a. (g) (1 Point) If P[X > b] = 0.24196, find b. (h) (1 Point) If P[2 < X ≤ c] = 0.01234, find c. (i) (1 Point) Find P[|X - μ| < kσ] for k = 1, 2, 3. (j) (1 Point) Find the value of integer k for which P[X > μ + kσ] = 10^-j for j = 1, 2, 3, 4, 5.

          Let X be a Gaussian random variable with mean μ = -4 and variance σ^2 = 16, i.e., X ~ N(-4, 16). Compute the following probabilities (give numerical answers):

(a) (1 Point) P[X > 4].
(b) (1 Point) P[|X| < 4].
(c) (2 Points) P[X > -4|X < 4].
(d) (1 Point) P[X < 4|X > -4].
(e) (1 Point) P[X > 4|X > -4].
(f) (1 Point) If P[X < a] = 0.8869, find a.
(g) (1 Point) If P[X > b] = 0.24196, find b.
(h) (1 Point) If P[2 < X ≤ c] = 0.01234, find c.
(i) (1 Point) Find P[|X - μ| < kσ] for k = 1, 2, 3.
(j) (1 Point) Find the value of integer k for which P[X > μ + kσ] = 10^-j for j = 1, 2, 3, 4, 5.

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