# Suppose X is the waiting time (in minutes) for a bus and its p. d. f. is given by f(x) = {15 for 0≤x≤50 otherwise.Find the probability that waiting time is between 1 and 3 minutes - Mathematics and Statistics

Sum

Suppose X is the waiting time (in minutes) for a bus and its p. d. f. is given by

f(x) = {(1/5,  "for"  0 ≤ x ≤ 5),(0,  "otherwise".):}
Find the probability that waiting time is between 1 and 3 minutes

#### Solution

waiting time is between 1 and 3 minutes,

= P(1 < X < 3) = int_1^3 f(x)*dx

= int_1^3 (1)/(5)*dx

= (1)/(5) int_1^3 1*dx

= (1)/(5)[x^2]_1^3

= (1)/(5)[3 - 1]

= (2)/(5).

Concept: Probability Distribution of a Continuous Random Variable
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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 8 Probability Distributions
Exercise 8.2 | Q 1.06 | Page 145