Five males with a particular genetic disorder have one child each. The random variable x is the number of children among the five who inherit the genetic disorder. Determine whether the table describes a probability distribution. If it​ does, find the mean and standard deviation.

x
0
1
2
3
4
5

​P(x)
0.0010
0.0146
0.0879
0.2637
0.3955
0.2373
Find the mean of the random variable x. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
muequals
​(Round to one decimal place as​ needed.)
B.
The table is not a probability distribution.
Find the standard deviation of the random variable x. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
sigmaequals
​(Round to one decimal place as​ needed.)
B.
The table is not a probability distribution.

ok Can you please help me?

To determine whether the table describes a probability distribution, we need to check if the probabilities sum up to 1. Let's calculate the sum of the probabilities:

0.0010 + 0.0146 + 0.0879 + 0.2637 + 0.3955 + 0.2373 = 1

Since the probabilities sum up to 1, the table is a probability distribution.

To find the mean (average) of the random variable x, we multiply each value of x by its corresponding probability, and then sum up these products.

Mean (μ) = (0 * 0.0010) + (1 * 0.0146) + (2 * 0.0879) + (3 * 0.2637) + (4 * 0.3955) + (5 * 0.2373)
= 0 + 0.0146 + 0.1758 + 0.7911 + 1.582 + 1.1865
= 3.75 (rounded to two decimal places)

Therefore, the mean of the random variable x is 3.75.

To find the standard deviation of the random variable x, we need to calculate the variance first. The variance (σ^2) is calculated by finding the squared difference of each value of x from the mean, multiplying it by its corresponding probability, and summing up these products.

Variance (σ^2) = [(0 - 3.75)^2 * 0.0010] + [(1 - 3.75)^2 * 0.0146] + [(2 - 3.75)^2 * 0.0879] + [(3 - 3.75)^2 * 0.2637] + [(4 - 3.75)^2 * 0.3955] + [(5 - 3.75)^2 * 0.2373]

= [(-3.75)^2 * 0.0010] + [(-2.75)^2 * 0.0146] + [(-1.75)^2 * 0.0879] + [(-0.75)^2 * 0.2637] + [(-0.25)^2 * 0.3955] + [(1.25)^2 * 0.2373]

= 14.0625 * 0.0010 + 7.5625 * 0.0146 + 3.0625 * 0.0879 + 0.5625 * 0.2637 + 0.0625 * 0.3955 + 1.5625 * 0.2373

= 0.0140625 + 0.1100575 + 0.26746875 + 0.14786375 + 0.02471875 + 0.37096875

= 0.93514 (rounded to five decimal places)

The standard deviation (σ) is the square root of the variance.

Standard deviation (σ) = √(0.93514)
= 0.9663 (rounded to four decimal places)

Therefore, the standard deviation of the random variable x is 0.9663.

To determine whether the table describes a probability distribution, we need to check if the probabilities sum up to 1 and if all probabilities are non-negative.

Let's calculate the sum of the probabilities:
0.0010 + 0.0146 + 0.0879 + 0.2637 + 0.3955 + 0.2373 = 1

The sum of the probabilities is 1, which means the table describes a probability distribution.

Now, let's calculate the mean of the random variable x. The mean is calculated by multiplying each value of x by its corresponding probability and summing them up.

Mean (μ) = Σ (x * P(x))

0 * 0.0010 + 1 * 0.0146 + 2 * 0.0879 + 3 * 0.2637 + 4 * 0.3955 + 5 * 0.2373 = 2.5

So, the mean of the random variable x is 2.5.

Now let's calculate the standard deviation of the random variable x. The standard deviation is a measure of the dispersion of the values around the mean and is calculated using the formula:

Standard Deviation (σ) = sqrt(Σ [(x - μ)^2 * P(x)])

0.0010 * (0 - 2.5)^2 + 0.0146 * (1 - 2.5)^2 + 0.0879 * (2 - 2.5)^2 + 0.2637 * (3 - 2.5)^2 + 0.3955 * (4 - 2.5)^2 + 0.2373 * (5 - 2.5)^2

Calculating this expression gives us approximately 1.23.

So, the standard deviation of the random variable x is approximately 1.23.

Therefore, the correct choices are:
A. The mean (µ) equals 2.5
A. The standard deviation (σ) equals 1.23.

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