6. Suppose a college professor never finishes her lecture before the end of the class period, and always finishes within three minutes after the class period is supposed to end. Let X = time that elapses between the end of the class period and the actual end of the lecture. Suppose the pdf of X is f(x) = kx² 0 < x < 3 and 0 otherwise. Find the value of k that makes f(x) a legitimate probability density function, and use that value of k to find the probability that the lecture ends within 1 minute after the class period is supposed to end.

Q: Verify that h(x) = = 8 3x³ 0 1≤x≤2 otherwise is a valid probability density function.

A: The probability density function is given by,

Q: Compute P(B|A) and P(A|B).

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Q: 2. if f(x) is a probability density function of a continuous random variable, then ...... ...dx = 88

A: Step 1: Step 2: Step 3: Step 4:

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Q: (b) Construct and sketch the cumulative distribution function.

A: Solution:

Q: 3. Let A be a parameter. Show that the family of functions fa(x) = x >0 is a probability density…

A:

Q: 5. Suppose that the current stock price is 100 $. Its annualized volatility is 25 % and return 15 %…

A:

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Q: Let P(A) = r and P(B) = s with AN B= p. Then P(A\B) equals Select one: а. 1 b. 1-5 C. 0 d. r

A: NOTE:  We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: If the moment generating function of a random variable Y is Find the probability density function of…

A:

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A:

Q: The probability density function of X, the lifetime of a certain type of device (measured in…

A: The PDF of random variable X is given by:

Q: Suppose that the random variables X and Y have the following joint probability density func f(x, y)…

A: Given: fx, y=ce-6xe-3y               0&lt;y&lt;x

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A:

Q: Let 0 be a parameter. Show that the family of functions fo(x) = x >0 à probability density function.…

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A:

Q: 7. Let X be a continuous random variable with probability density function given by Se-(z-z0) x > x0…

A: Let X be the continuous random variable with probability density function is,  f(x) = { e^-(x-x0)…

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A: Given:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.