Directions: Find (by inspection) the expected value and variance of the exponential random variable with the density function given below. 1. Expected Value: E(X) 2. Variance: Var (X) = f(2)=1/12e-²/2
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Solution is not 1/4 and 1/2
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- Martian potatoes begin to sprout very quickly after planting. Suppose X is the number of days after planting until a Martian potato sprouts. Then X has the following probability density function: f(x)= 2/7e−x + 3/14e−x/2 + 1/14e−x/4 for 0 ≤ x ≤ ∞ and 0 otherwise. d) What is the expected value of X (E(X))? e) What is the expected value of X2 ? f) What is the variance of X?Martian potatoes begin to sprout very quickly after planting. Suppose X is the number of days after planting until a Martian potato sprouts. Then X has the following probability density function: f(x)= 2/7e−x + 3/14e−x/2 + 1/14e−x/4 for 0 ≤ x ≤ ∞ and 0 otherwise. f) What is the variance of X? g) What is the standard deviation of X? h) What is the probability that X is more than 2 standard deviations above its expected value?