The statement some dogs are brown has 16 letters. Choose one of these 16 letters uniformly at random (i. e., with equal probability). Let X denote the length of the word containing the chosen letter. Determine the possible values and probability mass function of X.

Rx = {5,4,3}

The probability mass function can be formulated like this:

Px (3) = p (X = 3) = 3/16

Px (4) = p (X = 4) = 8/16

Px (5) = p (X = 5) = 5/16

Step-by-step explanation:

We have that the probability of choosing a letter (1) at random from the sentence would be 1/16.

We must first finish the length of each word:

some = 4 letters

dogs = 4 letters

are = 3 letters

brown = 5 letters

Therefore, the possible values, that is, the range would be:

Rx = {5,4,3}

since the range has finite set, then the random variable X is discrete random variable

now to find the probability mass function of X and it can be defined as:

Px (X) = P (X = x); where x = 3, 4, 5

Px (3) = p (X = 3)

It will be equal sum of probalities of all the letters that can form the three letter word "are" by letters A, R, E

Probability of getting length 3 when a letter is drawm from the some dogs are brown:

1/16 + 1/16 + 1/16 = 3/16

Px (4) = p (X = 4)

It will be equal sum of probalities of all the letters that can form the four letter word "some" and "dogs" by letters S, O, M, E, D, O, G, S

Probability of getting length 4 when a letter is drawm from the some dogs are brown:

1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16 +1/16 + 1/16 = 8/16

Px (5) = p (X = 5)

It will be equal sum of probalities of all the letters that can form the five letter word "brown" by letters B, R, O, W, N

Probability of getting length 5 when a letter is drawm from the some dogs are brown:

1/16 + 1/16 + 1/16 + 1/16 + 1/16 = 5/16

X             3             4              5

p(X)       3/16        8/16          5/16

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3

3xy cannot be combined with the others

2x, -5x and x are like terms