The variance of the probability distribution is 400
The Variables of X and their Probability Distribution.
To find Variance, first we should find out Mean and then Variance
The expected value of a discrete random variable X, symbolized as E(X), is often referred to as the long-term average or mean (symbolized as μ)
The variance of a probability distribution is symbolized as σ2. To find the variance σ2 of a discrete probability distribution, find each deviation from its expected value, square it, multiply it by its probability, and add the products.
Step – 1: Calculation of Mean Step – 2: Calculation of Standard Deviation= σ2=∑(x−μ)²P(x)
Mean = X * P(X) Variance = Sum of (X – Mean)²*P(X)
X P(X) X*P(X)
-50 0.029 -1.45
-30 0.121 -3.63
-10 0.210 -2.1
10 0.485 4.85
30 0.145 4.35
50 0.010 0.5
Mean 2.52
X P(X) X - Mean (X – Mean)² (X – Mean)²*P(X)
-50 0.029 -52.52 2758.35 79.99216
-30 0.121 -32.52 1057.55 127.9636
-10 0.210 -12.52 156.7504 32.91758
10 0.485 7.48 55.950 27.13594
30 0.145 27.48 755.1504 109.4968
50 0.019 47.48 2254.35 22.5435
Variance=400.00
Read more about variance at the below link: https://brainly.com/question/27271235
#SPJ10
