Question

1.5.4. Let $p_X(x)$ be the pmf of a random variable $X$. Find the cdf $F(x)$ of $X$ and sketch its graph along with that of $p_X(x)$ if: (a) $p_X(x) = 1$, $x = 0$, zero elsewhere. (b) $p_X(x) = frac{1}{3}$, $x = -1, 0, 1$, zero elsewhere. (c) $p_X(x) = frac{x}{15}$, $x = 1, 2, 3, 4, 5$, zero elsewhere.

          1.5.4. Let $p_X(x)$ be the pmf of a random variable $X$. Find the cdf $F(x)$ of $X$ and sketch its graph along with that of $p_X(x)$ if:
(a) $p_X(x) = 1$, $x = 0$, zero elsewhere.
(b) $p_X(x) = frac{1}{3}$, $x = -1, 0, 1$, zero elsewhere.
(c) $p_X(x) = frac{x}{15}$, $x = 1, 2, 3, 4, 5$, zero elsewhere.

$1.5.4. Let pX(x) be the pmf of a random variable X. Find the cdf F(x) of X and sketch its graph along with that of pX(x) if: (a) pX(x) = 1, x = 0, zero elsewhere. (b) pX(x) = frac13, x = -1, 0, 1, zero elsewhere. (c) pX(x) = fracx15, x = 1, 2, 3, 4, 5, zero elsewhere.$

Added by Cristina G.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Ameer Said

03/23/2022

Step 1

Step 1:** For part (a) where $ p_X(z) = 1, 0 \text{ elsewhere} $, we can find the CDF $ F(z) $ by integrating the PDF: \[ F(z) = \int_{-\infty}^{z} p_X(x) dx = \int_{-\infty}^{z} 1 dx = \begin{cases} 0 & \text{if } z < 0 \\ z & \text{if } z \geq 0 \end{cases} Show more…

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1.5.4. Let pX(x) be the pmf of a random variable X. Find the cdf F(x) of X and sketch its graph along with that of pX(x) if: (a) pX(x) = 1, x = 0, zero elsewhere. (b) pX(x) = 1/3, x = -1, 0, 1, zero elsewhere. (c) pX(x) = x/15, x = 1, 2, 3, 4, 5, zero elsewhere.