Let the random variable X denote the number of girls in a five-child family. Ifthe probability of a female birth is 0.5,21.(A) Find the probability of 0, 1, 2, 3, 4, and 5 girls in a five-child family.(B) Construct the binomial distribution and draw the histogram associated withthis experiment.al 2sr 3namhegxs end rd behogoua fon 2sw misb aynegmp siff.(e)A bnod 10 soie coubauensatong s baiato oicoso xie nad 15 Wa(C) Compute the mean and the standard deviation of the random variable X.

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Asked Dec 4, 2019
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Let the random variable X denote the number of girls in a five-child family. If
the probability of a female birth is 0.5,
21.
(A) Find the probability of 0, 1, 2, 3, 4, and 5 girls in a five-child family.
(B) Construct the binomial distribution and draw the histogram associated with
this experiment.
al 2sr 3namhegxs end rd behogoua fon 2sw misb aynegmp siff.
(e)
A bnod 10 soi
e coubaue
nsatong s baiato oicoso xie nad 15 Wa
(C) Compute the mean and the standard deviation of the random variable X.
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Let the random variable X denote the number of girls in a five-child family. If the probability of a female birth is 0.5, 21. (A) Find the probability of 0, 1, 2, 3, 4, and 5 girls in a five-child family. (B) Construct the binomial distribution and draw the histogram associated with this experiment. al 2sr 3namhegxs end rd behogoua fon 2sw misb aynegmp siff. (e) A bnod 10 soi e coubaue nsatong s baiato oicoso xie nad 15 Wa (C) Compute the mean and the standard deviation of the random variable X.

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Expert Answer

Step 1

21.

 

A.

 

From the given information, the random variable X denotes the number of girls in a five-child family and the probability of female birth is 0.5.

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P(X=0): Р(Х - 0)- 0.5°х 0.5° = 0.0313 P(X=1): -0рo5 -ая 0.5' P(X =1)= = 0.1563 P(X=2): 05 х0.5 P(X = 2)= =0.3125 P(X=3): -9)»в 0.5' х0.5* P(. = 0.3125 P(X=4): -)oя 0.5* x0.5 P(X =4)= = 0.1563 P(X=5): -Вля P(X =5)= 0.5 = 0.0313

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Step 2

B)

 

The random variable X denotes the number of girls in a five-child family and follows Binomial distribution with parameters n =5 and p = 0.50.

 

The probability mass function for the random variable X is,

 

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P(x-=)-ora-pr P(X =x)=(P) (p)* (1– p)™* * - (0.50) (1-0.50) -()0so)(a5" . (0.50) (0.5)*,x = 0,1, 2,. 5

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Step 3

Steps to construct Histogram in Excel:

 

  • Select the data in excel
  • Go to insert Menu
  • Go to insert column or Bar chart
  • click on clus...
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Histogram 0.35 0.3 0.25 0.2 0.15 0.1 0.05 3.

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