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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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One benefit of cluster sampling is that it Group of answer choices
luda_lava [24]

Answer:

a. is effective for use in school research.

Step-by-step explanation:

Cluster sampling is the sampling whereby we pick random few sample from the population to serve as the sample population called cluster. This cluster usually have uniform characteristics among them.

The main advantage of cluster sampling is that it is effective school research because of its cheapness and doesn't require much resources during the sampling process.

The other options are not correct because Cluster sampling have High sampling error and its biased sample.

3 0
3 years ago
½x + 1 ⅔ subtracted from 1 ½x - 1 ⅓<br> simplify IF NEEDED!!
beks73 [17]

Answer:

x-3

Step-by-step explanation:

8 0
3 years ago
How many feet are 8 2/3 (in fractions)
11Alexandr11 [23.1K]
<span>8.66666666666. I'm not sure if there are any more 6's.</span>
3 0
3 years ago
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Answer 7 and 8 and give the example please
maks197457 [2]
7. For this one, we need an equation. Lets make x = the price of the computer. Since the price of the printer is 30% the price of the computer, we can make that .3x, because a number multiplied by .3 will give you 30% of your original number. So, our equation will be:
x + .3x = 2028 \\ 1.3x = 2028 \\ x = 1560
Since x is the cost of the computer, you have your answer right there. The computer costs $2,028.


8. For this one we're going to need a proportion, but first we need to find out how much of the percentage of seeds Cliff planted. 
% of seeds planted per person:
Ali - 40
Ben - 45
Cliff - x
All percentages add up to 100, so we'll make an equation to figure this out:
40 + 45 + x = 100 \\ 85 + x = 100 \\ x = 15
Therefore, Cliff planted 15% of the seeds. Since Cliff planted 15% of the seeds, and he planted 87 total, 15% of our total number of seeds planted is 87. We can now make a proportion to figure out how many seedlings were planted all together.
\frac{87}{x} =  \frac{15}{100}
We can now cross multiply in order to get a solvable equation:
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Sorry if this is confusing at all, hope I helped!
3 0
3 years ago
A building in New York is 423 feet tall. The building next to it is 52% taller. How tall is the second building? Show or explain
Neko [114]

Answer:

642.96 ft

Step-by-step explanation:

first building 423 feet tall, that is 100% --> 423 ft

next building 100% + 52% = 152%

second building: so now we multiply (423 * 152%) or ( 423 * 152/100 )

answer is 642.96 ft

7 0
2 years ago
Read 2 more answers
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