How can I get results in the red box?
2026-03-26 12:52:07.1774529527
Conditional variance problem on INTRODUCTION TO PROBABILITY(2nd edition)
98 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in CONDITIONAL-PROBABILITY
- Given $X$ Poisson, and $f_{Y}(y\mid X = x)$, find $\mathbb{E}[X\mid Y]$
- Finding the conditional probability given the joint probability density function
- Easy conditional probability problem
- Conditional probability where the conditioning variable is continuous
- probability that the machine has its 3rd malfunction on the 5th day, given that the machine has not had three malfunctions in the first three days.
- Sum of conditional probabilities equals 1?
- Prove or disprove: If $X | U$ is independent of $Y | V$, then $E[XY|U,V] = E[X|U] \cdot E[Y|V]$.
- Conditional probability and binomial distribution
- Intuition behind conditional probabilty: $P(A|B)=P(B\cap A)/P(B)$
- Transition Probabilities in Discrete Time Markov Chain
Related Questions in VARIANCE
- Proof that $\mathrm{Var}\bigg(\frac{1}{n} \sum_{i=1}^nY_i\bigg) = \frac{1}{n}\mathrm{Var}(Y_1)$
- $\{ X_{i} \}_{i=1}^{n} \thicksim iid N(\theta, 1)$. What is distribution of $X_{2} - X_{1}$?
- Reason generalized linear model
- Variance of $\mathrm{Proj}_{\mathcal{R}(A^T)}(z)$ for $z \sim \mathcal{N}(0, I_m)$.
- Variance of a set of quaternions?
- Is the usage of unbiased estimator appropriate?
- Stochastic proof variance
- Bit of help gaining intuition about conditional expectation and variance
- Variance of $T_n = \min_i \{ X_i \} + \max_i \{ X_i \}$
- Compute the variance of $S = \sum\limits_{i = 1}^N X_i$, what did I do wrong?
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
It is a well-known fact that the variance of a uniformly distributed random variable on the interval $(a, b)$ is given by $(b - a)^{2}/12$. This can be shown using the Law of the Unconscious Statistician.
So,
$$\text{var}(X \mid Y = 1) = \frac{(1)^{2}}{12} = \frac{1}{12}$$
$$\text{var}(X \mid Y = 2) = \frac{(2)^{2}}{12} = \frac{4}{12} $$