MHT CET · Maths · Probability
The p.d.f. of c.r.v. \(X\) is given by \(f(x)=\frac{x+2}{18}\) if -2 < x < 4=0 otherwise then \(\mathrm{P}[|x| < 1]=\)
- A \(\frac{1}{18}\)
- B \(\frac{4}{9}\)
- C \(\frac{2}{9}\)
- D \(\frac{1}{9}\)
Answer & Solution
Correct Answer
(C) \(\frac{2}{9}\)
Step-by-step Solution
Detailed explanation
(A)
\(f(x)=\frac{x+2}{18}, -2 < x < 4 \)
\( =0, \text { otherwise } \)
\( P(|x| < 1)=P(-1 < x < 1) =\int_{-1}^{1} \frac{x+2}{18} \mathrm{dx} \)
\( =\int_{-1}^{1} f(x) d x=\frac{1}{18}\left[\frac{1}{2}+2-\frac{1}{2}+2\right]=\frac{4}{18}=\frac{2}{9}\)
\(f(x)=\frac{x+2}{18}, -2 < x < 4 \)
\( =0, \text { otherwise } \)
\( P(|x| < 1)=P(-1 < x < 1) =\int_{-1}^{1} \frac{x+2}{18} \mathrm{dx} \)
\( =\int_{-1}^{1} f(x) d x=\frac{1}{18}\left[\frac{1}{2}+2-\frac{1}{2}+2\right]=\frac{4}{18}=\frac{2}{9}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The plane through the intersection of planes \(x+y+z=1\) and \(2 x+3 y-z+4=0\) and parallel to Y-axis also passes through the pointMHT CET 2023 Medium
- The general solution of the differential equation \(\sec ^{2} x\) tany \(d x+\sec ^{2} y \tan x d y=0\)
isMHT CET 2020 Easy - The area bounded by the circle \(x^{2}+y^{2}=16\) and lines x=0 and x=2 isMHT CET 2020 Medium
- Two adjacent of sides parallelogram \(\mathrm{ABCD}\) are given by \(\overline{\mathrm{AB}}=2 \hat{i}+10 \hat{j}+11 \hat{k}\) and \(\overline{\mathrm{AD}}=-\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+2 \hat{\mathrm{k}}\). The side \(\mathrm{AD}\) is rotated by angle \(\alpha\) in plane of parallelogram so that \(\mathrm{AD}\) becomes \(\mathrm{AD}^{\prime}\). If \(\mathrm{AD}^{\prime}\) makes a right angle with the side \(A B\), then the cosine of the angle \(\alpha\) is given byMHT CET 2023 Hard
- The principal solutions of \(\sqrt{3} \sec x+2=0\) areMHT CET 2021 Medium
- If the angle between the planes \(x-2 y+3 z-5=0\) and \(x+\alpha y+2 z+7=0\) is \(\cos ^{-1}\left(\frac{1}{14}\right)\) then the difference between the values of \(\alpha\) isMHT CET 2025 Medium
More PYQs from MHT CET
- An inclined plane makes an angle \(30^{\circ}\) with the horizontal. A solid sphere rolling down an inclined plane from rest without slipping has linear acceleration ( \(g=\) acceleration due gravity) \(\left(\sin 30^{\circ}=0.5\right)\)MHT CET 2025 Medium
- Match the types of endosperms given in Column I with examples given in Column II
Column I Column II i. Cellular a. Coconut ii. Nuclear b. Asphodelus iii. Helobial c. Petunia MHT CET 2024 Medium - Which from following solids is isotropic?MHT CET 2025 Easy
- A mass tied to a string is whirled in a horizontal circular path with a constant angular velocity and its angular momentum is L. if the string is now halved, keeping angular velocity same, then the angular momentum will beMHT CET 2022 Medium
- The mutual inductance (M) of the two coils is \(3 \mathrm{H}\). The self inductances of the coils are \(4 \mathrm{H}\) and \(9 \mathrm{H}\) respectively. The coefficient of coupling between the coils isMHT CET 2023 Medium
- \(\int \frac{x+1}{x^{2}+5 x+6} d x=\)MHT CET 2020 Easy