TS EAMCET · Maths · Probability
If X is a random variable with probability distribution \(\mathrm{P}(\mathrm{X}=k)=\frac{(2 k+3) \mathrm{c}}{3^k}\), \(k=0,1,2, \ldots\), to \(\infty\), then \(\mathrm{P}(\mathrm{X}=3)=\)
- A \(\frac{1}{24}\)
- B \(\frac{1}{18}\)
- C \(\frac{1}{6}\)
- D \(\frac{1}{3}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{18}\)
Step-by-step Solution
Detailed explanation
\(\sum_{k=0}^{\infty} \mathrm{P}(\mathrm{X}=k) = 1 \) \(\mathrm{c} \sum_{k=0}^{\infty} \frac{2 k+3}{3^k} = 1 \) \(\mathrm{c} \left( 2 \sum_{k=0}^{\infty} k \left(\frac{1}{3}\right)^k + 3 \sum_{k=0}^{\infty} \left(\frac{1}{3}\right)^k \right) = 1 \)…
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
- If the angle between the circles and is then a value of isTS EAMCET 2020 Hard
- The probability distribution of a random variable \(X\) is given below.
Then the variance of \(X\) isTS EAMCET 2011 Easy - If \(x=\frac{2 a t}{1+t^2}, y=\frac{a\left(1-t^2\right)}{1+t^2}\), where \(t\) is a parameter, then \(a\) isTS EAMCET 2019 Medium
- \(\int_{\frac{-\pi}{2}}^{\frac{\pi}{2}} \sin ^2 x \cos ^2 x(\sin x+\cos x) d x=\)TS EAMCET 2023 Medium
- If the Circumcenter of the triangle formed by the points \(A(a, 3), B(b, 5)\) and \(C(a, b)\) is \((1,1)\), then out of all the possible coordinates of \(\mathrm{C}\) the sum of the absolute values of the distinct coordinates of \(\mathrm{C}\) isTS EAMCET 2023 Easy
- If \(\mathrm{OA}=6 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-4 \hat{\mathrm{k}}, \mathrm{OB}=2 \hat{\mathbf{j}}+\hat{\mathrm{k}}\), OC \(=5 \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) are the coterminous edges of a parallelopiped, then the height of the parallelopiped drawn from the vertex \(A\) isTS EAMCET 2019 Medium
More PYQs from TS EAMCET
- The relation between the coefficient of real expansion \(\left(\gamma_r\right)\) and coefficient of apparent expansion \(\left(\gamma_a\right)\) of a liquid and the coefficient of linear expansion \(\left(\alpha_g\right)\) of the material of the container isTS EAMCET 2005 Hard
- The number of even numbers greater than 1000000 that can be formed using all the digits \(1,2,0,2,4,2\) and 4 isTS EAMCET 2019 Easy
- A particle moves over a plane with a constant acceleration . At the time the velocity is The speed of the particle when it is displaced by parallel to the -axis is,TS EAMCET 2021 Medium
- X-rays of wavelength \(0.140 \mathrm{~nm}\) are scattered from a block of carbon. What will be the wavelengths of \(X\)-rays scattered at \(90^{\circ}\) ?TS EAMCET 2008 Medium
- \(\lim _{x \rightarrow 8} \frac{\sqrt{1+\sqrt{1+x}}-2}{x-8}\) is equal toTS EAMCET 2011 Medium
- If the angle \(\theta\) between the vectors \(\overrightarrow{\mathbf{a}}=2 x^2 \hat{\mathbf{i}}+4 x \hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(\overrightarrow{\mathbf{b}}=7 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+x \hat{\mathbf{k}}\) is such that \(90^{\circ} < \theta < 180^{\circ}\), then \(x\) lies in the intervalTS EAMCET 2010 Hard