Let X denote the distance (m) that an animal moves from its birth site to the...

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 m

(b) What is the probability that distance exceeds the mean distance by more than 2 standard deviations? (Round your answer to four decimal places.)

(c) What is the value of the median distance? Hint: Find a such that

P(X≤a)= 0.50

(Round your answer to two decimal places.)

(d) Only 5% of animals will move farther than what distance? Hint: Find a such that

P(X≤a)= 0.95

. (Round your answer

Expert Solution

orchestra answered 2 years ago

Let X denote the distance (m) that an animal moves from its birth site to the...

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 (in meters) that an animal moves from its birth site to...

Let X denote the distance (in meters) 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 θ = 72.46. Find the probability that the distance is: a) at most 100 meters b) at most 200 meters c) between 100 and 200 meters

Let X = the distance (in meters) that a small animal moves from its birthplace to...

Let X = the distance (in meters) that a small animal moves from its birthplace to the first territorial vacancy it encounters. Suppose that for a specific species X has a uniform distribution with a mean of 75 meters and a standard deviation of 10 meters. a) What is the probability that the distance is at most 100 m? At most 200m? b) What is the probability that the distance is between 100m and 200m? c) What is the probability...

A car moves along an x axis through a distance of 980 m, starting at rest...

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?

Let X = NN endowed with the product topology. For x ∈ X denote x by...

Let X = NN endowed with the product topology. For x ∈ X denote x by (x1, x2, x3, . . .). (a) Decide if the function given by d : X × X → R is a metric on X where, d(x, x) = 0 and if x is not equal to y then d(x, y) = 1/n where n is the least value for which xn is not equal to yn. Prove your answer. (b) Show that no...

Suppose there are two sources that cause pollution at a receptor site. Let e denote emissions...

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...

Let R be a ring (not necessarily commutative), and let X denote the set of two-sided...

Let R be a ring (not necessarily commutative), and let X denote the set of two-sided ideals of R. (i) Show that X is a poset with respect to to set-theoretic inclusion, ⊂. (ii) Show that with respect to the operations I ∩ J and I + J (candidates for meet and join; remember that I+J consists of the set of sums, {i + j} where i ∈ I and j ∈ J) respectively, X is a lattice. (iii) Give...

Will Smith consumes chocolate and milk. Let y denote chocolate and x denote milk. Chocolate has...

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 =...

A fair 4-sided die is rolled, let X denote the outcome. After that, if X =...

A fair 4-sided die is rolled, let X denote the outcome. After that, if X = x, then x fair coins are tossed, let Y denote the number of Tails observed. a) Find P( X >= 3 | Y = 0 ). b) Find E( X | Y = 2 ). “Hint”: Construct the joint probability distribution for ( X, Y ) first. Write it in the form of a rectangular array with x = 1, 2, 3, 4 and...

1. Let M denote set of m&ms in a bag. This consist of red, yellow, green,...

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...

Question

Let X denote the distance (m) that an animal moves from its birth site to the...

Solutions

Expert Solution

Related Solutions

Let X denote the distance (m) that an animal moves from its birth site to the...

Let X denote the distance (in meters) that an animal moves from its birth site to...

Let X = the distance (in meters) that a small animal moves from its birthplace to...

A car moves along an x axis through a distance of 980 m, starting at rest...

Let X = NN endowed with the product topology. For x ∈ X denote x by...

Suppose there are two sources that cause pollution at a receptor site. Let e denote emissions...

Let R be a ring (not necessarily commutative), and let X denote the set of two-sided...

Will Smith consumes chocolate and milk. Let y denote chocolate and x denote milk. Chocolate has...

A fair 4-sided die is rolled, let X denote the outcome. After that, if X =...

1. Let M denote set of m&ms in a bag. This consist of red, yellow, green,...