Determine whether a probability distrubution is given, in thosecases where a pro

Question

Determine whether a probability distrubution is given, in thosecases where a probability distribution is not described, identifythe requirements that are not satisfied. in those cases whereit is described find its mean and standard deviation

8. A researcher reports that when groups of four childrenare randomly selected from a population of couples meeting certaincriteria. the probability distribution for the numbers of girls isas given in the accompanying table.

X     P(x)

0       .4219

1       .4219

2       .1406

3      .0156

Please help me out I'm confusesd on how to start this off.

Explanation / Answer

Consider the following table x x^2 p(x) x*P(x) x^2*p(x) 0 0 0.4219 0 0 1 1 0.4219 0.4219 0.4219 2 4 0.1406 0.2812 0.5624 3 9 0.0156 0.0468 0.1404 1 0.7499 1.1247 x x^2 p(x) x*P(x) x^2*p(x) 0 0 0.4219 0 0 1 1 0.4219 0.4219 0.4219 2 4 0.1406 0.2812 0.5624 3 9 0.0156 0.0468 0.1404 1 0.7499 1.1247
Since the total probability = 1 therefore we can saythat the given one is the probability distribution Mean = xP(x)           =0.7499 Standard deviation =[ x2P(x) -(mean)2]                               =[1.1247-(0.7499)2 ]                               =0.7499 x x^2 p(x) x*P(x) x^2*p(x) 0 0 0.4219 0 0 1 1 0.4219 0.4219 0.4219 2 4 0.1406 0.2812 0.5624 3 9 0.0156 0.0468 0.1404 1 0.7499 1.1247

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