A six-sided dice is rolled in a gambling game. The number on the side facing up is denoted by a random variable X. If the number $P(X = i) = c \times i$, where $c$ is a positive real constant and $i \in \{1, 2, 3, 4, 5, 6\}$. (a) Find is the value of $c$. (b) Find the probability mass function of X. (c) What is the expectation and variance of X ? (d) What are the $E[(4X + 1)^2]$ and $Var[5 - 2X]$?
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- A six-sided dice is rolled with possible outcomes i ∈ {1, 2, 3, 4, 5, 6} - The probability function is given as P(X = i) = c × i, where c is a constant Show more…
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