If random variable X is the waiting time in m | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The probability density function is given by $f(x) = \frac{1}{5}$ for $0 \leq x \leq 5$ and $0$ otherwise.We need to find the probability that the

Vedclass · Accepted Answer

$0.8$

Vedclass · Answer

(B) The probability density function is given by $f(x) = \frac{1}{5}$ for $0 \leq x \leq 5$ and $0$ otherwise.We need to find the probability that the waiting time $X$ is not more than $4$ minutes,which is $P(X \leq 4)$.This is calculated by integrating the probability density function from the lower bound to $4$:$P(X \leq 4) = \int_{0}^{4} f(x) \, dx$$P(X \leq 4) = \int_{0}^{4} \frac{1}{5} \, dx$$P(X \leq 4) = \left[ \frac{x}{5} \right]_{0}^{4}$$P(X \leq 4) = \frac{4}{5} - \frac{0}{5} = \frac{4}{5} = 0.8$Therefore,the probability is $0.8$.

Similar Questions

In a hospital, on an average if there are $35$ births in a week, then the probability that there will be less than $3$ births in a day is:

$A$ random variable $X$ has its range $\{-1, 0, 1\}$. If its mean is $0.2$ and $P(X=0)=0.2$,then $P(X=1)=$

Let $X$ denote the sum of the numbers obtained when two fair dice are rolled. Find the variance and standard deviation of $X$.

Three balls are drawn at random from a bag containing $5$ blue and $4$ yellow balls. Let the random variables $X$ and $Y$ respectively denote the number of blue and yellow balls. If $\bar{X}$ and $\bar{Y}$ are the means of $X$ and $Y$ respectively,then $7 \bar{X} + 4 \bar{Y}$ is equal to ..........

Find the probability distribution of the number of heads in four tosses of a coin.

Vedclass Test Series

Exam Paper Generator

Online Exam Module