TS EAMCET · Maths · Statistics
Let \(X \sim B(n, p)\) with mean \(\mu\) and variance \(\sigma^2\). If \(\mu=2 \sigma^2\) and \(\mu+\sigma^2=3\), then \(P(X \leq 3)=\)
- A \(\frac{15}{16}\)
- B \(\frac{2}{3}\)
- C \(\frac{14}{17}\)
- D \(\frac{1}{3}\)
Answer & Solution
Correct Answer
(A) \(\frac{15}{16}\)
Step-by-step Solution
Detailed explanation
As we know that, mean \(=\mu=n p\) and variance \(=\sigma^2=n p q\) Since it is given that, \(\mu=2 \sigma^2\) \(\Rightarrow \quad n p=2 n p q \Rightarrow q=\frac{1}{2} \quad \therefore p=1-q=\frac{1}{2}\) and as \(\mu+\sigma^2=3\) \(\Rightarrow \quad n p+n p q=3\)…
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 \(\triangle A B C\) is right angled at \(A\), then \(r_2+r_3\) is equal toTS EAMCET 2002 Hard
- If and , thenTS EAMCET 2021 Easy
- For the system \(S\) of linear equations \(x+y+z=3,2 x+2 y-z=3, x+y+\lambda z=1\) the incorrect option among the following statements isTS EAMCET 2020 Easy
- The numerically greatest term in the binomial expansion of \((2 x-3 y)^5\) when \(x=\frac{3}{2}\) and \(y=\frac{2}{3}\) isTS EAMCET 2023 Medium
- For \(n>2\) and \(n \in \mathbf{N}\), the product of the roots of \((x-n)\left(\left(x^2-2 n x\right)^2+\left(2 n^2-5\right)\left(x^2-2 n x\right)\right.\) \(\left.+\left(n^4-5 n^2+4\right)\right)=0\) is divisible byTS EAMCET 2020 Medium
- If is a matrix such that thenTS EAMCET 2021 Easy
More PYQs from TS EAMCET
- The points whose position vectors are \(2 \mathbf{i}+3 \mathbf{j}+4 \mathbf{k}, 3 \mathbf{i}+4 \mathbf{j}+2 \mathbf{k}\) and \(4 \mathbf{i}+2 \mathbf{j}+3 \mathbf{k}\) are the vertices ofTS EAMCET 2013 Easy
- The molar conductivity of 0.02 M solution of an electrolyte is \(124 \times 10^{-4} \mathrm{~S} \mathrm{~m}^2 \mathrm{~mol}^{-1}\). What is the resistance of the same solution (in ohms), kept in a cell of cell constant \(129 \mathrm{~m}^{-1} ?\)TS EAMCET 2024 Medium
- Let \(f(0)=1, f(0.5)=\frac{5}{4}, f(1)=2, f(1.5)=\frac{13}{4}\) and \(f(2)=5\). Using Simpson's rule, \(\int_0^2 f(x) d x\) is equal toTS EAMCET 2011 Hard
- Which one of the following gives yellow precipitate with iodine and \(\mathrm{NaOH}\) solution?TS EAMCET 2010 Easy
- At \(27^{\circ} \mathrm{C}, 500 \mathrm{~mL}\) of helium diffuses in 30 minutes. What is the time (in hours) taken for \(1000 \mathrm{~mL}\) of \(\mathrm{SO}_2\) to diffuse under same experimental conditions?TS EAMCET 2004 Easy
- Which of the following compounds has the highest standard molar entropy?TS EAMCET 2021 Easy