Assume b, c are independent random variables with uniform distribution on the interval [-L, L), where L e R'. Find the probability that the solutions of the quadratic equation x? + bx + c= 0 are real. What happens when L → +0?

Q: Let X1,...,X, be a random sample from (1+ 0x) f(x) = 2 ,-1< x < 1, -1 < 0 < 1. Find the consistent…

A: The random sample consists of X1,X2,...,Xn. Need to obtain: The consistent estimator of θ. The…

Q: Let X be a discrete random variable with moment generating function given by: Mx (1) = (0.21+0.79e¹)…

A: Given that Moment generating function of X is Mx(t)=(0.21+0.79et)18.

Q: Katelyn wants to buy a new cell phone. She decides to buy an iPhone 8 for a price of $449.99. She…

A:

Q: At the end of summer, the total weight of seeds accumulated by a nest of seed-gathering ants will…

A: Since you’ve posted a question with multiple sub-parts, we will solve the first 3 sub-parts and…

Q: how would you calculate a-d of question 2?

A: We will calculate one by one in the following manner from the given data:

Q: Suppose we have the quadratic function f(x)=A(x^2)+C where the random variables A and C have…

A: A quadratic equation is written as f(x)=Ax2+Bx+C. f(x) has real roots if B2-4AC≥0.

Q: 12. Let X be a normal random variable with mean 678 and standard deviation 8.85. Let Q₁ the…

A:

Q: Use the probability generating functions to derive the formula for the average small components size…

A: To derive the formula for the average small component size when GC is present using probability…

Q: -, P(T|R) P(RT) 9 Consider two events R and T. Find- 1)P(R' UT) = ? = 3 2/7,P( ,P(ROT) = 116 8

A: From the provided information,

Q: The random variable B is normally distributed with mean zero and unit variance. Find the probability…

A: The mentioned quadratic equation is, X2+2BX+1=0 Here, B is a normally distributed variable with a…

Q: Suppose we have the quadratic function f(x)=A(x^2)+2X+C where the random variables A and C have…

A: Let the quadratic equation is f(x)=Ax2+2X+C. From the question, f(A)=A2     0≤A≤2 f(C)=3C2    0≤C≤1…

Q: P(C|m')

A:

Q: he life X (in years) of a voltage regulator of a car has the pdf f(x) = cx²e (²)³, x>0 a) Find c.…

A: Please note that as per our guidelines if multiple questions are posted we can answer the first…

Q: Let A, B, and C be independent random variables, uniformly distributed on (0, 1). What is the…

A:

Q: Let X1, X2, . .., Xn be a random sample from a population with a pdf a+2022 (a+ 2021) () ; х > 0, а…

A:

Q: Derive the MGF for an exponential random variable X ~ exp(A) (try the Kernel trick!) O eta t-入…

A:

Q: Suppose that P(A') = 0.4, P(B') = 0.5, P(An B) = 0.4. Find P(A), P(B), P(AUB), P(An B') and P(AIB).

A: given data P(A') =0.4P(B') = 0.5P(A∩B) = 0.4

Q: If P(A) + P(B) = 0.9 and P(ANB) = 0.2, then what is the value of P(An B')

A: Given the conditions ( P(A) + P(B) = 0.9 ) and (P(A∩B)=0.2), we're asked to find the value…

Q: A continuous random variable X has the PDF fx(x)=kx2, 0 < ? < 1. a) What is the value of k ? b) Find…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: If the odds against R occurring are 1:7, then find P(R) and P(R'). P(R)= (Simplify your answer.)…

A: For the defined event R, the odds using the ratio against R occurring is given as: No. of…

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!