{"id":20320,"date":"2024-04-15T05:51:18","date_gmt":"2024-04-15T05:51:18","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=20320"},"modified":"2024-04-15T05:51:18","modified_gmt":"2024-04-15T05:51:18","slug":"consider-a-random-variable-to-which-a-poisson-distribution-is-best-fitted-it-happens-that-px-1-frac23px-2-on-this-distribution-plot-the-variance-of-this-distribution-will-be-a-3","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/consider-a-random-variable-to-which-a-poisson-distribution-is-best-fitted-it-happens-that-px-1-frac23px-2-on-this-distribution-plot-the-variance-of-this-distribution-will-be-a-3\/","title":{"rendered":"Consider a random variable to which a Poisson distribution is best fitted. It happens that P(x = 1) = $$\\frac{2}{3}$$P(x = 2) on this distribution plot. The variance of this distribution will be A. 3 B. 2 C. 1 D. $$\\frac{2}{3}$$"},"content":{"rendered":"

[amp_mcq option1=”3″ option2=”2″ option3=”1″ option4=”$$\\frac{2}{3}$$” correct=”option1″]<\/p>\n

The correct answer is $\\boxed{\\text{B}}$.<\/p>\n

A Poisson distribution is a probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known average rate and independently of the time since the last event.<\/p>\n

The variance of a Poisson distribution is equal to its mean. In this case, we are given that $P(x = 1) = \\frac{2}{3}P(x = 2)$. This means that the mean of the distribution is $\\mu = 2$. The variance of the distribution is therefore $\\sigma^2 = \\mu = 2$.<\/p>\n

Here is a brief explanation of each option:<\/p>\n