Question:
Let a random variable $\mathrm{X}$ have a binomial distribution with mean 8 and variance 4 .
If $\mathrm{P}(\mathrm{x} \leq 2)=\frac{\mathrm{k}}{2^{16}}$, then $\mathrm{k}$ is equal to :
17
1
121
137
Correct Option: , 4
Solution:
$\mathrm{np}=8$
$\mathrm{npq}=4$
$\mathrm{q}=\frac{1}{2} \Rightarrow \mathrm{p}=\frac{1}{2}$
$\mathrm{n}=16$
$\mathrm{p}(\mathrm{x}=\mathrm{r})=16 \mathrm{C}_{\mathrm{r}}\left(\frac{1}{2}\right)^{16}$
$\mathrm{p}(\mathrm{x} \leq 2)=\frac{{ }^{16} \mathrm{C}_{0}+{ }^{16} \mathrm{C}_{1}+{ }^{16} \mathrm{C}_{2}}{2^{16}}$
$=\frac{137}{2^{16}}$
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,
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