Question

I'f di = xi -13 , fidi = 30 and fi = 120 then x is equal to ?
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Answer 1

Answer:

The value of x is 13.25

Hope it's crt

Answer 2

Answer:

x = 7, 19, or 25

Step-by-step explanation:

Use the formula for the variance of a discrete random variable: The variance of a discrete random variable X with possible values x1, x2, ..., xn and corresponding probabilities p1, p2, ..., pn is given by:

Var(X) = sum(pi * (xi - E(X))^2)

where E(X) is the expected value of X.

Find the expected value of X: We can find the expected value of X using the formula:

E(X) = sum(pi * xi)

Since we are not given the probabilities directly, we can use the information given in the problem to find the probabilities. We know that fidi = 30, which means that the sum of (xi - 13) * 120 = 30. Simplifying this equation gives:

xi - 13 = 0.25

xi = 13.25

Therefore, the expected value of X is:

E(X) = (120/360) * (13.25) + (120/360) * (13.25) + (120/360) * (13.25) = 13.25

Use the formula for the variance of X: Using the formula for the variance of X and the expected value we found in step 2, we have:

Var(X) = (1/3) * (x1 - 13)^2 + (1/3) * (x2 - 13)^2 + (1/3) * (x3 - 13)^2

where x1, x2, and x3 are the three possible values of X.

We are given that fi = 120 for all three possible values of X. Since the sum of the probabilities is 1, each probability is 1/3. Therefore, we have:

120 = (1/3) * fi = (1/3) * 120 = 40

Solve for X: We can use the information we have gathered to write three equations:

x1 - 13 = sqrt((30/40) * (x1 - 13)^2)

x2 - 13 = sqrt((30/40) * (x2 - 13)^2)

x3 - 13 = sqrt((30/40) * (x3 - 13)^2)

Simplifying these equations gives:

x1 - 13 = 0.75 * (x1 - 13)

x2 - 13 = 0.75 * (x2 - 13)

x3 - 13 = 0.75 * (x3 - 13)

Solving for x1, x2, and x3 gives:

x1 = 19

x2 = 7

x3 = 25

Therefore, the value of x is one of the possible values of X, which is:

x = 7, 19, or 25

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