The probability detibution of tho random variable X represents the number of hit

Question

The probability detibution of tho random variable X represents the number of hits a baseball player obsined in a game for the 2012 basbal season The probability striutin was used along wih Sinsical soltware to smulate 25 ropeiios ofthe xpriment 25 games) T based on the simulation. The simudation was repesated by peirfoming 50 repeticns of the esperiment Approxinao the mean and The nunbor ofwded Approale the mean and standard devation of the ndom vaable X standard deviation of the random varable Compare your esuts to he de-iation what property is being ??strated? EB Click the Icon to view the data tables Compute the theoretical mean of the random variable X for lthe given prabablity distrbuon heoeical mean and standed Round to three decimal places as needed ) Compute the theoretical standard devlation of the ranmable X o thegven probabiliay detribution (Round to three decimal places an needed ) #xt hits Round to three decimal places as needed)

Explanation / Answer

Solution:-
a) Mean = µ? = ?x P(x)
= (0*0.1239)+(1*0.3633)+(2*0.2224)+(3*0.2157)+(4*0.0153)+(5*0.0594)
= 1.813 hits

?x = 1.279 hits

b) For n = 25
µ? = 1.813
  
?x = 1.279/sqrt(25) = 0.256

c) For n = 50
µ? = 1.813
  
?x = 1.279/sqrt(50) = 0.181

d) option C. The law of large numbers

  

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