The probability distribution of random variable, X, is defined as follows: X 0 1 2 3 4
Probability 0 0.3 0.1 0.3 0.3
A) Explain if the above is a valid probability model.
B) Is the described random variable discrete or continuous?
C) What is the expected value (mean) of the probability distribution?
D) Calculate P(X = 3).
E) Calculate P(X < 4).
F) Calculate P(X > 0).
G) Calculate P(X = 5).
H) Calculate P(X = 0).
I) What is the total area under any density curve?

Answer and Step-by-step explanation:

A) For the model to be a probability distribution, it has to follow two conditions:

1) The probability of each value of the discrete random variable is between, and included, 0 and 1:

2) The sum of all probabilities is 1;

In the table shown, the probabilities are from 0 to 0.3 - between 0 and 1;

Adding the probabilities: 0 + 0.3 + 0.1 + 0.3 + 0.3 = 1

Therefore, this model is a valid probability distribution model.

B) They are discrete because each value correspond to a finite number of possible values.

C) Expected value is calculated by

E(X) = 2.6

D) P(X=3) = P(3), which means probability of 3:

P(X=3) = 0.3

E) P(X<4): probabilities of values of X that are less than 4:

P(X<4) = P(0) + P(1) + P(2) + P(3)

P(X<4) = 0 + 0.3 + 0.1 + 0.3

P(X<4) = 0.7

F) P(X>0) = P(1) + P(2) + P(3) + P(4)

P(X>0) = 0.3 + 0.1 + 0.3 + 0.3

P(X>0) = 1

G) P(X=5) = P(5)

There is no probability of P(5) because the model doesn't "cover" that number.

H) P(X=0) = P(0)

P(X=0) = 0

I) The total area of any density curve is 1 because it represents all the possible values a variable can assume.

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

55? i think maybe

step-by-step explanation: