Topic: Finding the Mean and the Variance of Discrete Probability Distribution. In this lesson, we shall learn how to find the mean and the variance as well as the standard deviation of a probability distribution. But before we proceed, let us recall first how to find the mean and standard deviation a frequency distribution by doing the next activities. The mean ( X) of a frequency distribution is obtained by using the formula X = ZN Where X = mean f= frequency N = total frequency Complete Table 3.1 below, and compute the mean by using the formula given above. Table 3.1 Ages of Grade 11 mathematics Teachers 4 N T 1. What is the value of N? 2. What is the value of _ fx ? 3. What is the value of the mean X ? B. The variance (o2 ) and the standard deviation ( o ) of a frequency distribution are computed by using the following formulas: 82 = NEfx 2 - (Efx) 2 " = NEf x2 -(Efx)2ad Qualitative Research Where N = total frequency f = frequency X = score Compute the variance and the standard deviation of the following distribution by using the above formulas and completing the table below. Table 3.2 Ages of Grade 11 Mathematics Teachers LL N + NH Analyze and Explore: Just like frequency distribution, the probability distribution can be described by computing its mean and variance of a discrete probability distribution. The Mean of a Discrete probability DistributionFind the mean of the following probability distributions. Complete the table. P(H) H. P(H) IO 0.06 0.70 0.20 0.03 0.01 Find the variance and the standard deviation of the following probability distributions. Complete the table. I P(H) H.P(H) H2 . P(H) O 0.06 0.70 N 0.20 0.03 0.01