Construct your own table showing probability distribution using 8 data. Solve for mean, variance and standard deviation of the distribution.

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Clara Clark · Accepted Answer

Step 1 Introduction:  Random Variable: A random variable is a real valued function that assign a real number to each outcome (i.e., sample point) of a random experiment. Random variable divided into two types they are  - Discrete random variable - A random variable say &quot;x&quot;, which can take finite number of values in the interval of                                                       domain  - Continuous random variable - A random variable say &quot;x&quot;, which can take any value in its domain or in an interval.  The Mean (expected value) of the random variable x is denoted by E[X]  i.e. E[X]=∑i=1nxip(xi)  The Variance of the random variable x is denoted by Var[X]  i.e., Var[X]=E[X2]−(E[X])2  Here E[X2]=∑i=1nxi2p(xi)  and Standard deviation =Var[X]  Step 2 Answer and explanation:  Consider the following table:  xp(x)00.110.320.130.240.130.120.210.4  Here x is a random variable and p(x) is a probability distribution.  The mean of the random variable x is  E[X]=(0⋅0.1)+(1⋅0.3)+(2⋅0.1)+(3⋅0.2)+(4⋅0.1)+(3⋅0.1)+(2⋅0.2)+(1⋅0.4) where i=0,1,2,3,4,3,2,1  =0+0.3+0.2+0.6+0.4+0.3+0.4+0.4  =2.4  Therefore, the mean of the random variable x is E[X]=2.4  The Variance of the random variable x is  Var[X]=E[X2]−(E[X])2  Now, E[X2]=(02⋅0.1)+(12⋅0.3)+(22⋅0.1)+(32⋅0.2)+(42⋅0.1)+(32⋅0.1)+(22⋅0.2)+(12⋅0.4)  =(0⋅0.1)+(1⋅0.3)+(4⋅0.1)+(9⋅0.2)+(16⋅0.1)+(9⋅0.1)+(4⋅0.2)+(1⋅0.4)  =0+0.3+0.4+1.8+1.6+0.9+0.8+0.4  =6.2  then

Construct your own table showing probability distribution using 8 data.

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