Which definition of probability is NOT applicable if the events of a random experiment are not equally likely?
Classical definition
The **Classical definition** of probability assumes that all outcomes of a random experiment are equally likely. If the events are not equally likely, this definition is not applicable. The Empirical, Axiomatic, and Bayesian definitions can handle events with unequal likelihoods.
Similar Questions
Let the joint probability density function of \( (X, Y) \) be
\[f(x, y) = \begin{cases} 6xy^2 & \text{if } 0 < x < 1, 0 < y < 1 \\ 0, & \text{otherwise} \end{cases}\]
Then \( P\left(\frac{1}{2} < X < \frac{3}{4}\right) \) is:
Let X and Y have the joint p.m.f. f(x, y) = x + y / 21, where x = 1, 2, 3 and y = 1, 2. The marginal p.m.f. of X is:
For a random variable X following Poisson distribution with parameter 5, the variance of X is:
If \( n \) is a natural number, then, for what value of \( k \) is the following function a probability mass function?
\[ f(x) = \frac{n!}{x!(n-x)!}k^{x}(1-k)^{n-x}, \quad x = 0,1,2,\ldots,n \]
Let \( X \) have pdf:
\[ f(x) = \begin{cases} \frac{3(2x - x^2)}{4} & \text{for } 0 \leq x \leq 2, \\ 0, & \text{otherwise} \end{cases} \]
Then the mode is equal to:
A random variable X is distributed at random between the values 0 and 1 in such a way that the PDF of X is f(x) = x2(1 - x3), where k is a constant. The value of k is:
If the first two raw moments of X are equal to zero, then P(X = 0) is equal to:
Let the probability density function of \( X \) be:
\[ f(x) = \begin{cases} 3(1-x)^2 & \text{for } 0 \leq x \leq 1 \\ 0 & \text{otherwise} \end{cases} \]
Then \( P\left(\frac{1}{2} < X < \frac{3}{4}\right) \) is equal to:
Let the probability mass function of \( X \) be given by:
\[ p(x) = c \frac{4^x}{x!}, \quad x = 0,1,2,3, \ldots \]Then the constant \( c \) is equal to:
In an industry, the risk of suffering from occupational disease is 20%. The probability that out of 6 workers, four will suffer from the disease is:
Important Questions from Probability Distribution
Which of the following are the properties of Binomial distribution?
A. May be symmetrical or skewed
B. Uni-modal, bell-shaped and symmetrical
C. Asymptotic to the x-axis
D. n and p are the two parameters
E. μ and σ are the two parameters
Choose thecorrectanswer from the options given below:
The following two statements relate to probability distributions. Choose the correct code for the statements being correct or incorrect.
Statement I: When ‘p' and 'q' are equal in the binomial distribution, the shape of the distribution is perfectly symmetrical irrespective of the size of 'n'.
Statement II: The mean and the variance of Poisson distribution are not equal.
Which of the following are the properties of normal distribution?
(A) May be symmetrical or skewed
(B) Uni-modal, bell-shaped and symmetrical
(C) Asymptotic to the x-axis
(D) m and p are the two parameters
(E) μ and σ are the two parameters
Choose the correct answer from the options given below:
Let the joint probability density function of \( (X, Y) \) be
\[f(x, y) = \begin{cases} 6xy^2 & \text{if } 0 < x < 1, 0 < y < 1 \\ 0, & \text{otherwise} \end{cases}\]
Then \( P\left(\frac{1}{2} < X < \frac{3}{4}\right) \) is:
Let X and Y have the joint p.m.f. f(x, y) = x + y / 21, where x = 1, 2, 3 and y = 1, 2. The marginal p.m.f. of X is:
