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Rzqust [24]
3 years ago
12

Let X be the total number of individuals of an endangered lizard species that are observed in a region on a given day. This obse

rved number is assumed to be distributed according to a Poisson distribution with a mean of 3 lizards. The endangered lizards can belong to either of two sub-species: graham or opalinus. Let Y be the number of graham lizards observed during this study (note that the total observed number of any lizard is denoted by X, so the observed number of opalinus lizards is given by X − Y). It is known that graham lizards are by far the most common. In particular, the conditional distribution of the number of graham lizards (Y) given the total number of all lizards (X) is Binomial with parameters n = X and p = 0.8.
(a) Write down the joint probability mass function of (X, Y). As always, remember to state the range of x and y. Then compute the joint probability mass function when (x, y) = (2,1). [Hint: recall the formula for a conditional probability and note that we know the conditional probability and one of the marginal distributions].

(b) Calculate the mean and variance of Y. [Hint: use the law of iterated expectations and variances].

(c) Write down the formula for the joint (cumulative) distribution function of (X, Y) using your result in part (a). As always, remember to state the relevant ranges of x and y. Then compute the joint distribution function when x, y = (2,1). [Hint: when writing down the joint distribution function, recall that the value of Y must always be less than or equal to the value of X. If you are stuck on the second part, try making a table of the joint pmf of (X, Y) up to the values x, y = (2,1)].

(d) Write down the formula for the marginal probability mass function of Y. As always, remember to state the range of y.

(e) Note that Y is less than X with zero probability so that, for example, P(X = 0, Y = 1) = 0. Use this and the fact that P (Y=1) ≥ P(X=2, Y=1) to determine whether X and Y are independent. Carefully show your argument.
Mathematics
1 answer:
kenny6666 [7]3 years ago
8 0

Answer:its c

Step-by-step explanation:

that is how i would do it.

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How much water and how much drink mix should Jerome use to make enough energy drink for all the runners? Create a table to show
yanalaym [24]

Answer: First, you need to figure out 22 times 2 = 44. Then, you need to multiply the original ratio by 44 to get the answer.

Step-by-step explanation:

3 0
3 years ago
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Find the volume h=12cm r=5cm
Goshia [24]

If this was a cone, the volume would be 314.16.

  • You would just put in the radius and height in the cone volume formula which is πr²h 1/3

If this is a cylinder then the volume would be 942.48

  • Put in the radius and height in the cylinder volume formula which is πr²h
7 0
2 years ago
Given a force of 10N and an acceleration of 5m/s? What is the mass?
likoan [24]

Answer:

<h3>2kg = mass</h3>

Step-by-step explanation:

<h3>What is the mass?</h3>

Mass is a body of matter without definite shape.

Use the Newton's second law of motion formula.

Note: \longrightarrow \sf{F=M*A}

<u>Given:</u>

  • Force = 10N
  • Acceleration = 5m/s

First thing you do is divide.

10/5=2

= 2kg (mass)

Therefore, the final answer is 2kg (mass).

I hope this helps, let me know if you have any questions.

To learn more about the mass:

brainly.com/question/7580108

5 0
1 year ago
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attashe74 [19]

Answer:

3.1%

Step-by-step explanation:

6/196 × 100% = 3.1%

8 0
2 years ago
Graph a line with a slope of -3 that contains the point (4, -2)
Crank

Answer:

Step-by-step explanation:

Given that

Slope m=-3

A point (x, y)=(4,-2)

Equation of a line can generally be written as

y=mx+c

Where, m is the slope

And c is the intercept on y-axis

Since we are given m=-3

Then, y=mx+c becomes

y=-3x+c

To get c, let substitute the point given, i.e x=4 and y=-2

y=-3x+c

-2=-3(4)+c

-2=-12+c

-2+12=c

c=-2+12

c=10

y=mx+c, then m=-3 and c=10

Then, the equation the line becomes y = -3x + 10

This is the required line equation

5 0
3 years ago
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