Question

math 124 elementary stats - fall 2025 > assessment
cw 10/7 (random variables)
practice score: 0/1 answered: 0/1
question 1
for the following distribution:

x	1	2	3	4
p(x)	0.3	0.2	0.4	0.1

find the following probabilities:
a) (p(x = 2))
b) (p(x < 3))
c) (p(xgeq2))
d) calculate the expected value (mean)

Explanation:

Step1: Find $P(X = 2)$

The probability $P(X = 2)$ is directly given in the probability - distribution table. When $X = 2$, $p(x)=0.2$.

Step2: Find $P(X < 3)$

$P(X < 3)=P(X = 1)+P(X = 2)$. From the table, $P(X = 1)=0.3$ and $P(X = 2)=0.2$. So $P(X < 3)=0.3 + 0.2=0.5$.

Step3: Find $P(X\geq2)$

$P(X\geq2)=P(X = 2)+P(X = 3)+P(X = 4)$. From the table, $P(X = 2)=0.2$, $P(X = 3)=0.4$, $P(X = 4)=0.1$. So $P(X\geq2)=0.2 + 0.4+0.1 = 0.7$.

Step4: Calculate the expected value $E(X)$

The formula for the expected value of a discrete - random variable is $E(X)=\sum_{x}x\cdot p(x)$. So $E(X)=1\times0.3 + 2\times0.2+3\times0.4 + 4\times0.1=0.3+0.4 + 1.2+0.4=2.3$.

Answer:

a) $0.2$
b) $0.5$
c) $0.7$
d) $2.3$