1. An experiment involves rolling two dice and observing the number of dots on the upper face of each after they come to a stop. A random variable (r.v.) $X$ is defined as the product of the number of dots on the upper face of each dice, after they stop rolling. The dice are not fair and therefore have probabilities: $Pr\{1 \text{ dot}\} = 0.05$, $Pr\{2 \text{ dots}\} = 0.15$, $Pr\{3 \text{ dots}\} = 0.3$, $Pr\{4 \text{ dots}\} = 0.3$, $Pr\{5 \text{ dots}\} = 0.15$, $Pr\{6 \text{ dots}\} = 0.05$, a) Determine and plot the PMF $P_X(x)$ of the random variable $X$, b) Determine and plot the cumulative probability distribution function (c.p.d.f.) $F_X(x)$ of the random variable $X$ and specify it mathematically. c) Obtain the mean and the variance of the random variable. d) Are the events {$X > 6.2$} and {$X \le 16.7$} statistically independent?
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So, the possible values of $X$ are: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36. Show more…
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