Let X follows normal distribution with mean μ and median μ̃, then P(μ < X < μ̃) is equal to:
0
For a normal distribution, the mean and the median coincide, meaning that they are equal. Therefore, the probability of X being between the mean and the median (μ < X < μ̃) is 0, since there is no area between the mean and the median for a symmetric distribution.
Similar Questions
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:
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:
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:
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:
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:
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:
A discrete random variable X has the following probability distribution.
X 1 2 3 4 5 6 7 P(X) K 2K 2K 3K K 2 2K 2 7K 2 + K What is the value of K?
Match List - I with List - II :
List - I (Description) List - II (Term) A. The probability of both success and failure remains constant I. Binomial Distribution B. The mean of distribution may be negative or positive II. Poisson Distribution C. The sum of all probabilities is equal to 1 III. Normal Distribution D. The probability of occurrence of an outcome within a very small time period is very small IV. Random Variable Choose the correct answer from the options given below :
