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Studentka2010 [4]
3 years ago
12

Consider the random variables X and Y with joint density function ???? f(x,y)= x+y, 0≤x≤1;0≤y≤1 0, elsewhere. (a) Find the margi

nal distributions of X and Y . (b) Find P(X > 0.25,Y > 0.5).
Mathematics
1 answer:
sp2606 [1]3 years ago
7 0

a. The marginal densities

f_X(x)=\displaystyle\int_0^1(x+y)\,\mathrm dy=x+\frac12

and

f_Y(y)=\displaystyle\int_0^1(x+y)\,\mathrm dx=y+\frac12

b. This can be obtained by integrating the joint density over [0.25, 1] x [0.5, 1]:

P(X>0.25,Y>0.5)=\displaystyle\int_{1/4}^1\int_{1/2}^1(x+y)\,\mathrm dx\,\mathrm dy=\frac{33}{64}

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Solve for x in the diagram below (picture included)
Sever21 [200]

Answer:

34

Step-by-step explanation:

We know the straight line is equal to 180°, and the three angles that make it are (x+12),100°, and x. We can use the equation 180=(x+12)+100+x to find x.

180=(x+12)+100+x

We can remove the parentheses and combine x plus x to 2x.

180=100+2x+12

100+12=112

so

180=112+2x

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Find the product of 543.1187 and 100 A. 5.431187 B. 54,311.87 C. 5,431.187 D. 54.31187 Can someone also explain how they came up
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543.1187\times100=\boxed{54311.87}

When you're multiplying by a power of 10 such as 100, the decimal point moves two places to the right. Note that this corresponds with the number of zeroes in 100. Of course our number is going to get bigger, not smaller, which means we'd have to be going right. If we multiplied by something like 0.001, we'd also be going two places, just going smaller and to the left.
7 0
3 years ago
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Which sequences are arithmetic? Check all that apply.
spin [16.1K]

Answer:

3)    18, 5.5, –7, –19.5, –32, …   sequence is in Arithmetic Progression.

5)     16, 32, 48, 64, 80         sequence is in Arithmetic Progression.

Step-by-step explanation:

If, a, b, c ,k, e ... is a given sequence.

Then the above sequence is in AP if b - a   =  c - b = k - c = ...

or, each term has same COMMON DIFFERENCE (d).

Here, take each sequence and check for the value of d.

1) –5, 5, –5, 5, –5, …

Here, 5 - (-5)  = 10,   -5 - 5  = -10

and 10 ≠ -10.  So the sequence is NOT in Arithmetic Progression.

2)96, 48, 24, 12, 6

Here, 48 - 96  = -48,   24 - 48  = -24

and -48 ≠ -24.  So the sequence is NOT in Arithmetic Progression.

3)18, 5.5, –7, –19.5, –32, …

Here, 5.5 - 18 = -12.5    ,  -7 - 5.5 = -12.5  ..

and -12.5 is the common difference.  

So the sequence is in Arithmetic Progression.

4)–1, –3, –9, –27, –81, …

Here, -3-(-1)  =  - 2     -9 - (-3)  = -6

and -2 ≠ -6.  So the sequence is NOT in Arithmetic Progression.

5)16, 32, 48, 64, 80

Here, 32 - 16 = 16    ,  48  - 32= 16  ..

and 16 is the common difference.  

So the sequence is in Arithmetic Progression.

6 0
3 years ago
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mixas84 [53]
N = 7.81 (round to 2 decimal places)

7 0
3 years ago
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