Tom, Dorothy, and Sammy went on a vacation and agreed to split the costs evenly. During their trip Tom paid $105, Dorothy paid $
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Answer and Step-by-step explanation: For an exponential distribution, the probability distribution function is:
f(x) = λ.
and the cumulative distribution function, which describes the probability distribution of a random variable X, is:
F(x) = 1 -
(a) <u>Probability</u> of distance at most <u>100m</u>, with λ = 0.0143:
F(100) = 1 -
F(100) = 0.76
<u>Probability</u> of distance at most <u>200</u>:
F(200) = 1 -
F(200) = 0.94
<u>Probability</u> of distance between <u>100 and 200</u>:
F(100≤X≤200) = F(200) - F(100)
F(100≤X≤200) = 0.94 - 0.76
F(100≤X≤200) = 0.18
(b) The mean, E(X), of a probability distribution is calculated by:
E(X) =
E(X) =
E(X) = 69.93
The standard deviation is the square root of variance,V(X), which is calculated by:
σ =
σ =
σ = 69.93
<u>Distance exceeds the mean distance by more than 2σ</u>:
P(X > 69.93+2.69.93) = P(X > 209.79)
P(X > 209.79) = 1 - P(X≤209.79)
P(X > 209.79) = 1 - F(209.79)
P(X > 209.79) = 1 - (1 - )
P(X > 209.79) = 0.0503
(c) Median is a point that divides the value in half. For a probability distribution:
P(X≤m) = 0.5
= 0.5
= 0.5
=
= 0.5
= - 0.5
ln() = ln(0.5)
-0.0143.m = - 0.0693
m = 48.46
In order to rationalize the denominator of each expression, we need to multiply the expression by the same radical in the denominator, this way we can remove the radical from the denominator.
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