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Xis a random variable with uniform probability density function in the interval [-2,10], For Y = 2X- 6, the conditional probability P(Y< 7 I X > 5) (rounded off to three decimal places) is ____ .
Correct answer is '0.3'. Can you explain this answer?
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Xis a random variable with uniform probability density function in the...
x follows uniform distribution over [-2, 10]
∴
Given: y = 2x - 6
⇒
For y = 7
∴
Given: y = 2x - 6
⇒
For y = 7
Most Upvoted Answer
Xis a random variable with uniform probability density function in the...
= 4 | X = 2) is:
First, we need to find the value of Y when X = 2:
Y = 2X - 6 = 2(2) - 6 = -2
So, we want to find P(Y = 4 | X = 2), which is the probability that Y = 4 given that X = 2.
Using the formula for conditional probability:
P(Y = 4 | X = 2) = P(Y = 4 and X = 2) / P(X = 2)
Since X has a uniform probability density function in the interval [-2,10], its probability density function is:
fX(x) = 1 / 12, for -2 <= x=""><=>
Therefore, the probability of X = 2 is:
P(X = 2) = fX(2) * (10 - (-2)) = 1 / 12 * 12 = 1
Now, we need to find the joint probability P(Y = 4 and X = 2). Since Y = 2X - 6, we can solve for X in terms of Y:
X = (Y + 6) / 2
So, when Y = 4, we have:
X = (4 + 6) / 2 = 5
Therefore, P(Y = 4 and X = 2) = P(X = 5) = fX(5) * (10 - (-2)) = 1 / 12 * 12 = 1
Putting it all together:
P(Y = 4 | X = 2) = P(Y = 4 and X = 2) / P(X = 2) = 1 / 1 = 1
So, the probability that Y = 4 given that X = 2 is 1.
First, we need to find the value of Y when X = 2:
Y = 2X - 6 = 2(2) - 6 = -2
So, we want to find P(Y = 4 | X = 2), which is the probability that Y = 4 given that X = 2.
Using the formula for conditional probability:
P(Y = 4 | X = 2) = P(Y = 4 and X = 2) / P(X = 2)
Since X has a uniform probability density function in the interval [-2,10], its probability density function is:
fX(x) = 1 / 12, for -2 <= x=""><=>
Therefore, the probability of X = 2 is:
P(X = 2) = fX(2) * (10 - (-2)) = 1 / 12 * 12 = 1
Now, we need to find the joint probability P(Y = 4 and X = 2). Since Y = 2X - 6, we can solve for X in terms of Y:
X = (Y + 6) / 2
So, when Y = 4, we have:
X = (4 + 6) / 2 = 5
Therefore, P(Y = 4 and X = 2) = P(X = 5) = fX(5) * (10 - (-2)) = 1 / 12 * 12 = 1
Putting it all together:
P(Y = 4 | X = 2) = P(Y = 4 and X = 2) / P(X = 2) = 1 / 1 = 1
So, the probability that Y = 4 given that X = 2 is 1.
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Xis a random variable with uniform probability density function in the...
X follows uniform distribution over [-2, 10]
∴
Given: y = 2x - 6
⇒
For y = 7
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Xis a random variable with uniform probability density function in the interval [-2,10], For Y = 2X- 6, the conditional probability P(Y< 7 I X > 5) (rounded off to three decimal places) is ____ .Correct answer is '0.3'. Can you explain this answer?
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