1. >Probability
Found 3  QuestionsSET DEFAULT
Selected Filters
    Probability Probability Distributions
Exams
Subjects
Topics

List of top Probability Questions on Probability Distributions

Let \( X_1, X_2, \dots, X_{10} \) be a random sample from a probability density function

\[ f_\theta(x) = f(x - \theta), \quad -\infty<x<\infty, \]

where \( -\infty<\theta<\infty \) and \( f(-x) = f(x) \) for \( -\infty<x<\infty \). For testing

\[ H_0: \theta = 1.2 \quad \text{against} \quad H_1: \theta \neq 1.2, \]

let \( T^+ \) denote the Wilcoxon Signed-rank test statistic. If \( \eta \) denotes the probability of the event \( \{T^+<50\} \) under \( H_0 \), then \( 32\eta \) equals

\[ \underline{\hspace{2cm}} \]

(round off to 2 decimal places).
  • GATE ST - 2021
  • GATE ST
  • Probability
  • Probability Distributions
Let \( (X, Y) \) have the joint probability density function

\[ f_{X,Y}(x,y) = \begin{cases} \frac{4}{(x + y)^3}, & x>1, y>1 \\ 0, & \text{otherwise} \end{cases} \]

Then which one of the following statements is NOT true?
  • GATE ST - 2021
  • GATE ST
  • Probability
  • Probability Distributions
Let \( X \) be a random variable having the probability density function

\[ f(x) = \begin{cases} \frac{3}{13} (1 - x)(9 - x), & 0<x<1, \\ 0, & \text{otherwise}. \end{cases} \]

Then

\[ \frac{4}{3} E[(X^2 - 15X + 27)] \]

equals _________ (round off to 2 decimal places).
  • GATE ST - 2021
  • GATE ST
  • Probability
  • Probability Distributions