A probability density function must be defined on an interval. True False
It is true.
Probability density function is defined on continuous random variable.
A probability density function must be defined on an interval. True False
True or false? For a continuous function f(x) defined over the interval [a,b], the average value of the function will be "hit" somewhere inside the interval [a,b]
Let X be a continuous random variable defined on the interval [0, 4] with probability density function p(x) = c(1 + 4x) (a) Find the value of c such that p(x) is a valid probability density function. (b) Find the probability that X is greater than 3. (c) If X is greater than 1, find the probability X is greater than 2. (d) What is the probability that X is less than some number a, assuming 0 < a <...
The height of the probability density function of a uniformly distributed random variable is inversely proportional to the width of the interval it is distributed over True O False
True or False: a.) Probability density can never be negative. b.) The state f(x), a wave function can never be real (f(x)). c.)The state f(x), a wave function must be real number. d.) If z=z*, then z must be a real number. e.) integral from neg infinity to infinity of the wave function equals 1 for a real particle in a 1d system. f.) The product of a number and its complex conjugate is always a real number.
Find k such that the function is a probability density function over the given interval. Then write the probability density function. f(x) = kx2; (-1,4] Å f(x 1 / 2 (x) = 1 x ² O 3 64 7; f(x) = CS x2 2. 65
Is 0.5e^(−0.5x) a probability density function on the interval [0,∞)? If so, what kind of probability density function is it? What is its mean, median, variance, and standard deviation?
Answer True or False for the following questions: 1. The probability density function (pdf) is used to describe probabilities for continuous random variables. 2. The cumulative distribution function (cdf) gives the probability as an area. 3. The amount of time (beginning now) until an earthquake occurs has an uniform distribution 4. Normal distributions are commonly used in calculations of product reliability, or the length of time a product lasts. 6. The exponential distribution has the decay parameter, which says that...
9. A Rayleigh probability density function (pdf) does not include a direct path signal. True or False
4. Let X be a continuous random variable defined on the interval [1, 10 with probability density function r2 (a) Find the value of c such that p(x) is a valid probability density function. (b) Find the probability that X is larger than 8 or less than 2 (this should be one number! (c) Find the probability that X is larger than some value a, assuming 1 < a< 10 d) Find the probability that X is more than 3
3. Let X be a continuous random variable defined on the interval 0, 4] with probability density function p(r) e(1 +4) (a) Find the value of c such that p(x) is a valid probability density function b) Find the probability that X is greater than 3 (c) If X is greater than 1, find the probability X is greater than 2 d) What is the probability that X is less than some number a, assuing 0<a<4?