The probability distribution of a random variable \( X \) is given by:
Show Hint
- \( -1.8 \)
- \( -1 \)
- \( 1 \)
- \( 1.8 \)
The Correct Option is A
Solution and Explanation
To solve the problem, we need to compute the expected value \( E(X) \) of the given discrete probability distribution.
1. Use the Formula for Expected Value:
The expected value \( E(X) \) is given by:
\( E(X) = \sum [x_i \cdot P(x_i)] \)
2. Substitute the Given Values:
\[
E(X) = (-4)(0.1) + (-3)(0.2) + (-2)(0.3) + (-1)(0.2) + (0)(0.2)
\]
\[
= -0.4 + (-0.6) + (-0.6) + (-0.2) + 0
\]
\[
= -0.4 - 0.6 - 0.6 - 0.2 = -1.8
\]
3. Conclusion:
The expected value of the distribution is \( -1.8 \)
Final Answer:
The correct option is (A) -1.8.
Top CBSE CLASS XII Mathematics Questions
- 2, b, c are in A.P. and the range of determinant $\begin{vmatrix}1&1&1\\ 2&b&c\\ 4&b^{2}&c^{2}\end{vmatrix}$ is [2, 16]. Then find range of c is
- A committee of 11 members is to be formed from 8 males and 5 females. Let m denotes the number of ways of selecting committee having atleast 6 males and n denotes the number of ways of selecting atleast 3 females then
Determine whether each of the following relations are reflexive, symmetric, and transitive.
- Relation R in the set A={1,2,3,...13,14} defined as R={(x,y): 3x-y=0}.
- Relation R in the set of N natural numbers defined as R={(x,y): y=x+5 and x<4}.
- Relation R in the set A={1,2,3,4,5,6} defined as R={(x,y): y is divisible by x}.
- Relation R in the set of Z integers defined as R={(x,y): x-y is an integer}
- Relation R in the set of human beings in a town at a particular time given by
- R={(x,y): x and y work at same place}
- R={(x,y): x and y live in the same locality}
- R={(x,y): x is exactly 7 am taller that y}
- R={(x,y): x is wife of y}
- R={(x,y):x is father of y}
Show that the relation R in the set R of real numbers, defined as
R = {(a, b): a ≤ b2 } is neither reflexive nor symmetric nor transitive.Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as
R = {(a, b): b = a + 1} is reflexive, symmetric or transitive.
Top CBSE CLASS XII Probability Questions
- If \( P(A | B) = P(A' | B) \), then which of the following statements is true?
- In the following probability distribution, the value of p is:
- A coin is tossed three times. The probability of getting at least two heads is:
Four students of class XII are given a problem to solve independently. Their respective chances of solving the problem are: \[ \frac{1}{2},\quad \frac{1}{3},\quad \frac{2}{3},\quad \frac{1}{5} \] Find the probability that at most one of them will solve the problem.
The probability distribution of a random variable \( X \) is given below:
\( X \) 1 2 4 2k 3k 5k \( P(X) \) \( \frac{1}{2} \) \( \frac{1}{5} \) \( \frac{3}{25} \) \( \frac{1}{10} \) \( \frac{1}{25} \) \( \frac{1}{25} \)
Top CBSE CLASS XII Questions
- 2, b, c are in A.P. and the range of determinant $\begin{vmatrix}1&1&1\\ 2&b&c\\ 4&b^{2}&c^{2}\end{vmatrix}$ is [2, 16]. Then find range of c is
- A boy of mass 50 kg is standing at one end of a, boat of length 9 m and mass 400 kg. He runs to the other, end. The distance through which the centre of mass of the boat boy system moves is
- A capillary tube of radius r is dipped inside a large vessel of water. The mass of water raised above water level is M. If the radius of capillary is doubled, the mass of water inside capillary will be
- A circular disc is rotating about its own axis. An external opposing torque 0.02 Nm is applied on the disc by which it comes rest in 5 seconds. The initial angular momentum of disc is
- A circular disc is rotating about its own axis at uniform angular velocity \(\omega.\) The disc is subjected to uniform angular retardation by which its angular velocity is decreased to \(\frac {\omega}{2}\) during 120 rotations. The number of rotations further made by it before coming to rest is