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A joint sample space for two random variable X and Y has four elements (1, 1), (2, 2), (3, 3) and (4, 4). Probabilities of these elements are 0.1, 0.35, 0.05 and 0.5 respectively.
Que: The probability of the event {X ≤ 3} is
- a)0.45
- b)0.50
- c)0.55
- d)0.60
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A joint sample space for two random variable X and Y has four elements...
= 0.1+ 0.35 + 0.05 = 0.5
Most Upvoted Answer
A joint sample space for two random variable X and Y has four elements...
Joint Sample Space:
The joint sample space for two random variables X and Y consists of all possible outcomes or pairs of values that X and Y can take. In this case, the joint sample space has four elements: (1, 1), (2, 2), (3, 3), and (4, 4).
Probabilities:
The given probabilities for each element in the joint sample space are as follows:
- P((1, 1)) = 0.1
- P((2, 2)) = 0.35
- P((3, 3)) = 0.05
- P((4, 4)) = 0.5
Probability of the Event {X = 3}:
The event {X = 3} consists of all outcomes where X takes the value 3. From the joint sample space, we can see that there is only one outcome where X = 3, which is (3, 3).
To find the probability of the event {X = 3}, we need to sum up the probabilities of all outcomes in the joint sample space where X = 3.
Calculating the Probability:
P({X = 3}) = P((3, 3))
From the given probabilities, we can see that P((3, 3)) = 0.05.
Therefore, the probability of the event {X = 3} is 0.05.
Answer:
The correct answer is option 'B' - 0.50.
The joint sample space for two random variables X and Y consists of all possible outcomes or pairs of values that X and Y can take. In this case, the joint sample space has four elements: (1, 1), (2, 2), (3, 3), and (4, 4).
Probabilities:
The given probabilities for each element in the joint sample space are as follows:
- P((1, 1)) = 0.1
- P((2, 2)) = 0.35
- P((3, 3)) = 0.05
- P((4, 4)) = 0.5
Probability of the Event {X = 3}:
The event {X = 3} consists of all outcomes where X takes the value 3. From the joint sample space, we can see that there is only one outcome where X = 3, which is (3, 3).
To find the probability of the event {X = 3}, we need to sum up the probabilities of all outcomes in the joint sample space where X = 3.
Calculating the Probability:
P({X = 3}) = P((3, 3))
From the given probabilities, we can see that P((3, 3)) = 0.05.
Therefore, the probability of the event {X = 3} is 0.05.
Answer:
The correct answer is option 'B' - 0.50.
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A joint sample space for two random variable X and Y has four elements (1, 1), (2, 2), (3, 3) and (4, 4). Probabilities of these elements are 0.1, 0.35, 0.05 and 0.5 respectively.Que: The probability of the event {X ≤3} isa)0.45b)0.50c)0.55d)0.60Correct answer is option 'B'. Can you explain this answer?
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