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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 ≤ 2.5, Y ≤ 6} is
  • a)
    0.45
  • b)
    0.50
  • c)
    0.55
  • d)
    0.60
Correct answer is option 'A'. Can you explain this answer?
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Probability Calculation for Event {X < 2.5,="" y="" /> 6}

Given:
Joint sample space for two random variables 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.

To find the probability of the event {X < 2.5,="" y="" /> 6}, we need to determine the probability of each individual outcome that satisfies the given condition and sum them up.

Step 1: Identify the outcomes that satisfy the condition X < 2.5="" and="" y="" /> 6.

From the given joint sample space, we can see that there are no outcomes that satisfy the condition X < 2.5="" and="" y="" /> 6. Therefore, the probability of the event {X < 2.5,="" y="" /> 6} is 0.

Step 2: Calculate the probability of the event {X < 2.5,="" y="" /> 6}.

Since there are no outcomes that satisfy the given condition, the probability of the event {X < 2.5,="" y="" /> 6} is 0.

Answer: The probability of the event {X < 2.5,="" y="" /> 6} is 0.

Summary:
The event {X < 2.5,="" y="" /> 6} represents the joint occurrence of X being less than 2.5 and Y being greater than 6. However, from the given joint sample space, we can see that there are no outcomes that satisfy this condition. Therefore, the probability of this event is 0.
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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 ≤2.5, Y ≤ 6} isa)0.45b)0.50c)0.55d)0.60Correct answer is option 'A'. Can you explain this answer?
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