Question:
If X and Y are two random variables with the joint probability density function
\(f(x,y)=\left\{ \begin{array}{l} \frac{2}{3}(x+2y);\ \text{for}\ 0\lt x, y\lt 1 \\ 0;\ \ \ \ \ \ \ \ \ \ \text{otherwise} \end{array} \right.\)
then \(E[X|Y=\frac{1}{2}]\) will be
If X and Y are two random variables with the joint probability density function
\(f(x,y)=\left\{ \begin{array}{l} \frac{2}{3}(x+2y);\ \text{for}\ 0\lt x, y\lt 1 \\ 0;\ \ \ \ \ \ \ \ \ \ \text{otherwise} \end{array} \right.\)
then \(E[X|Y=\frac{1}{2}]\) will be
\(f(x,y)=\left\{ \begin{array}{l} \frac{2}{3}(x+2y);\ \text{for}\ 0\lt x, y\lt 1 \\ 0;\ \ \ \ \ \ \ \ \ \ \text{otherwise} \end{array} \right.\)
then \(E[X|Y=\frac{1}{2}]\) will be
Updated On: Jul 18, 2024
- \(\frac{5}{9}\)
- \(\frac{4}{9}\)
- \(\frac{1}{3}\)
- \(\frac{2}{3}\)
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
The correct option is (A) : \(\frac{5}{9}\).
Was this answer helpful?
0
0
Top Questions on Probability
- The probability of a boy winning a game is \( \frac{2}{3} \). Let \( n \) denote the least number of times he must play the game so that the probability of winning the game at least once is more than 90%, and \( X \) denotes that number of times he wins the game. Hence \( n \), mean, variance, and standard deviation of the random variable \( X \) are respectively:
(A) 3
(B) \( \frac{2}{3} \)
(C) 2
(D) 0.81
Choose the correct answer from the options given below:- CUET (UG) - 2024
- Mathematics
- Probability
- A coin is tossed twice. Then Match List-I with List-II:
List-I List-II (Adverbs) (A) P(exactly 2 heads) (I) \(\frac{1}{4}\) (B) P(at least 1 head) (II) \(1\) (C) P(at most 2 heads) (III) \(\frac{3}{4}\) (D) P(exactly 1 head) (IV) \(\frac{1}{2}\)
Choose the correct answer from the options given below :- CUET (UG) - 2024
- Mathematics
- Probability
- A pair of dice is rolled . If the two numbers appearing on them are different the probability that
Match List-I with List-II
LIST-I(EVENT) LIST-II(PROBABILITY) (A) The sum of the number is greater than 11 (i) 0 (B) The sum of the number is 4 or less (ii) 1/15 (C) The sum of the number is 4 (iii) 2/15 (D) The sum of the number is 4 (iv) 3/15 Choose the correct answer from the option given below
- CUET (UG) - 2024
- Mathematics
- Probability
- In a series of 4 trials, the probability of getting two successes is equal to the probability of getting three successes. The probability of getting at least one success is:
- CUET (UG) - 2024
- Mathematics
- Probability
- Two events \(X\) and \(Y\) are such that \(P(X) = \frac{1}{3}\), \(P(Y) = n\), and the probability of occurrence of at least one event is 0.8. If the events are independent, then the value of \(n\) is:
- CUET (UG) - 2024
- Mathematics
- Probability
View More Questions
Questions Asked in GATE XH-C1 exam
- In a particular code, if "RAMAN" is written as 52 and "MAP" is written as 33, then how will you code “CLICK" ?
- GATE XH-C1 - 2024
- Coding Decoding
- Fill in the blanks with the correct combination of tenses for the given sentence :
Darwin's work (i)_______ a related effect that (ii) ________ influenced the development of environmental politics - a 'decentering' of the human being.- GATE XH-C1 - 2024
- Fill in the Blanks
- In a certain type of code, 'they play cricket together' is written as ‘mv kb lb iv'; 'they score maximum points' is written as 'gb lb mb kv'; 'cricket score earned points' is written as 'mb gv kb kv' and 'points are earned together' is written as 'kv mv ob gv.'
What is the code for ‘earned maximum points’ ?- GATE XH-C1 - 2024
- Coding Decoding
- In a perfectly competitive market, suppose the market demand curve is given by P = 10 + W - Q, where P is the market price, W is the average wealth of the consumers in the market, and Q is the industry output. The total cost function for a representative firm is given by C(q) = q3 - 2q2 + 5q, where q is the output of a firm. If W = 80, then the total number of firms in this industry in the long-run will be ______ (in integer)
- GATE XH-C1 - 2024
- Demand curve
- Consider a duopoly market where Firm 1 and Firm 2 produce differentiated products such that the demand function of each firm is given by :
q1(p1, p2) = 18 - p1 + p2
q2(p1, p2) = 18 + p1 - p2
Here, q1 and q2 are the outputs produced by Firm 1 and Firm 2, respectively, and p1 and p2 are the corresponding per unit prices.
Cost of production for the ith firm is given by Ci(qi) = 2qi ∀ i = 1,2
The firms compete in prices. The price set by Firm 2 such that the market is in Nash equilibrium will be ________ (in integer).- GATE XH-C1 - 2024
- Demand curve
View More Questions