In: Math

Let X denote the distance (m) that an animal moves from its birth site to the first territorial vacancy it encounters. Suppose that for banner-tailed kangaroo rats, X has an exponential distribution with parameter λ = 0.01362.

(a) What is the probability that the distance is at most 100 m?

(b) What is the probability that distance exceeds the mean distance by more than 2 standard deviations?

(c) What is the value of the median distance? (Round your answer to two decimal places.)

Let X denote the distance (m) that an animal moves from
its birth site to the first territorial vacancy it encounters.
Suppose that for banner-tailed kangaroo rats, X has an
exponential distribution with parameter λ = 0.01452.
(a) What is the probability that the distance is at most 100 m?
At most 200 m? Between 100 and 200 m? (Round your answers to four
decimal places.)
at most 100 m
at most 200 m
between 100 and 200...

A car moves along an x axis through a distance of 980
m, starting at rest (at x = 0) and ending at rest (at
x = 980 m). Through the first 1/4 of that distance, its
acceleration is +3.00 m/s2. Through the next 3/4 of that
distance, its acceleration is -1.00 m/s2. What are
(a) its travel time through the 980 m and
(b) its maximum speed?

Suppose there are two sources that cause pollution at a receptor
site. Let e denote emissions and q denote abatement, or pollution
controlled.
Source
e
MAC
Plant
400
10 qp
Farm
200
10 qF
K ≡ concentration
K = 0.01ep + 0.02eF
a. What is concentration level at the receptor site without any
abatement?
Suppose the regulatory authority has chosen a target of 5.4.
b. What allocation would achieve this target? Is this a
cost-effective allocation?
c. What ambient charge...

Will Smith consumes chocolate and milk. Let y denote chocolate
and x denote milk. Chocolate has an unusual market where there is
only one supplier, and the more chocolate you buy from the
supplier, the higher the price she charges per unit. In fact,
y units of chocolate will cost Will y2
dollars. Milk is sold in the usual way at a price of 2 dollars per
unit. Will’s income is 20 dollars and his utility function is
U =...

1. Let M denote set of m&ms in a bag. This consist of red,
yellow, green, blue and brown candies.
a. Device on equivalence relation on M.
b. Define relation R on M by: aRb if and only if either: a is
green or b is blue, or, a is yellow abd b is not yellow. Is R
symmetric, reflexive, transitive or anti-symmetric? Explain.
2. On set Zx(Z not including {0}) define relation R (a,b) a,b e
Z, b#0 as...

: Let X denote the result of a random experiment with the
following cumulative distribution function (cdf): 0, x <1.5 | 1/
6 , 1.5<=x < 2 | 1/ 2, 2 <= x <5 | 1 ,x >= 5
Calculate ?(1 ? ≤ 6) and ?(2 ≤ ? < 4.5)
b. Find the probability mass function (pmf) of ?
d. If it is known that the result of the experiment is integer,
what is the probability that the result is...

Let the random variable X denote the time (hours) for which a
part is waiting for the beginning of the inspection process since
its arrival at the inspection station, and let Y denote the time
(hours) until the inspection process is completed since its arrival
at the inspection station. Since both X and Y measure the time
since the arrival of the part at the inspection station, always X
< Y is true. The joint probability density function for X...

Two fair dice are rolled at once. Let x denote the difference in
the number of dots that appear on the top faces of the two dice.
For example, if a 1 and a 5 are rolled, the difference is 5−1=4, so
x=4. If two sixes are rolled, 6−6=0, so x=0. Construct the
probability distribution for x. Arrange x in increasing order and
write the probabilities P(x) as simplified fractions.

Suppose two fair dice are rolled. Let X denote the product of
the values on the dice and Y denote minimum of the two dice.
Find E[X] and E[Y]
Find Var X and Var Y
Let Z=XY. Find E[Z].
Find Cov(X,Y) and Corr(X,Y)
Find E[X|Y=1] and E[Y|X=1]

The moon's diameter is 3.48 × 106 m, and its mean distance from
the earth is 3.85 × 108 m. The moon is being photographed by a
camera whose lens has a focal length of 70.0 mm. (a) Find the
diameter of the moon's image on the slide film. (b) When the slide
is projected onto a screen that is 17.1 m from the lens of the
projector (f = 170.0 mm), what is the diameter of the moon's image...

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