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. a)What is the probability that a Martian potato takes no more than 4 days to sprout? b) What is the probability that X >4? c) What is the probability that 2< X < 4?

Question

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.

a)What is the probability that a Martian potato takes no more than 4 days to sprout?

b) What is the probability that X >4?

c) What is the probability that 2< X < 4?

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?

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?

i) What is the expected value of

X4

?

j) What is the probability that X is within 1 standard deviation of its expected value?

k) What is the probability that X = .6?

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