Create an abstract image that symbolizes the statistical concepts described in the given question. Include three different graphical representations, corresponding to each scenario of the task. For the first scenario, show two uniform, discrete probability distributions, one ranging from 0 to 2, and the other from 3 to 4. For the second scenario, depict two continuous uniform distributions, again one from 0 to 2, and the other from 3 to 4. For the last scenario, illustrate two distinctly different probability density functions, indicating their independence. Do not include any text or numbers in the picture, let it convey the concept visually.

t the discrete random variable X be uniform on {0,1,2} and let the discrete random variable Y be uniform on {3,4}. Assume that X and Y are independent. Find the PMF of X+Y using convolution. Determine the values of the constants a, b, c, and d that appear in the following specification of the PMF.

pX+Y(z)=⎧⎩⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪a,b,c,d,0,z=3,z=4,z=5,z=6,otherwise.

a= - unanswered
b= - unanswered
c= - unanswered
d= - unanswered
Let the random variable X be uniform on [0,2] and the random variable Y be uniform on [3,4]. (Note that in this case, X and Y are continuous random variables.) Assume that X and Y are independent. Let Z=X+Y. Find the PDF of Z using convolution. The following figure shows a plot of this PDF. Determine the values of a, b, c, d, and e.

a=- unanswered
b=- unanswered
c=- unanswered
d=- unanswered
e=- unanswered
Let Xand Y be two independent random variables with the PDFs shown below. below.

fX(x)={5,0,if 0≤x≤0.1 or 0.9≤x≤1,otherwise.
fY(y)={1,0,if 0≤y≤1,otherwise.
Let W=X+Y. The following figure shows a plot of the PDF of W. Determine the values of a, b, c, d, e, f, and g.

a=- unanswered
b=- unanswered
c=- unanswered
d=- unanswered
e=- unanswered
f=- unanswered
g=- unanswered

Let the random variable X be uniform on [0,2] and the random variable Y be uniform on [3,4]

Determine the values of a, b, c, d, and e

a=0.5 b=3, c=4, d=5, e=6

For very first question answers will be as follow :

a=1/6
b=1/3
c=1/3
d=1/6

a=0.5 , b=3 ,c=4 ...

Let the random variable X be uniform on [0,2] and the random variable Y be uniform on [3,4]

Determine the values of a, b, c, d, and e

b=3, c=4, d=5, e=6

Let W=X+Y. The following figure shows a plot of the PDF of W. Determine the values of a, b, c, d, e, f, and g.

a=1, b=0.5, c=0.1

PLEASE post, IF ANYBODY KNOWS THE OTHER ANSWERS...

Hey Im trying to work out these questions, could you tell me how you obtained the aswers you got, to give me some light please for working out the others.

To find the PMF (Probability Mass Function) or PDF (Probability Density Function) of the sum of random variables using convolution, we need to convolve the PMFs or PDFs of the individual random variables.

First, let's consider the case of discrete random variables X and Y.

For X and Y independent, the PMF of X+Y is given by the convolution of their individual PMFs.

Given:
X is uniform on {0, 1, 2}
Y is uniform on {3, 4}

We can find the PMF of X using its uniform distribution, where each value has an equal probability of occurring.

pX(0) = pX(1) = pX(2) = 1/3

Similarly, for Y, each value has an equal probability since it is uniform.

pY(3) = pY(4) = 1/2

Now, to find the PMF of X+Y, we convolve the PMFs of X and Y.

pX+Y(z) = pX(0)*pY(z-0) + pX(1)*pY(z-1) + pX(2)*pY(z-2)

For z = 3, the convolution becomes:
pX+Y(3) = (1/3)(1/2) = 1/6

For z = 4, the convolution becomes:
pX+Y(4) = (1/3)(1/2) + (1/3)(1/2) = 1/3

For z = 5, the convolution becomes:
pX+Y(5) = (1/3)(1/2) = 1/6

For z = 6, the convolution becomes:
pX+Y(6) = 0 (since there is no combination of X and Y that sums to 6)

For all other values of z, pX+Y(z) = 0.

Therefore, the PMF of X+Y is given by:

pX+Y(z) = ⎧⎩⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪a,b,c,d,0,z=3,z=4,z=5,z=6,otherwise.

Here, the values of a, b, c, and d are still unanswered because they depend on the specific probabilities associated with each value of X and Y. To determine their values, you need to refer to the probabilities assigned to each value of X and Y in the problem statement.

The same approach can be applied to the other two problems involving continuous random variables by convolving their PDFs instead of PMFs. The values of a, b, c, d, e, f, and g will depend on the specific probabilities or probability densities assigned to each interval or value of X and Y given in the respective problem statements.

fX(x)={5,0,if 0≤x≤0.1 or 0.9≤x≤1,otherwise.

fY(y)={1,0,if 0≤y≤1,otherwise.
Let W=X+Y. The following figure shows a plot of the PDF of W. Determine the values of a, b, c, d, e, f, and g.

a= 1
b= 0.5
c= 0.1
d= 0.9
e= 1.1
f= 1.9
g= 2