The probability density function of a mixed random variable X is as follows: Af(x) 0.108(41) 0.20 8(x) 9,085(x-1) X a) Find the value of the constant a b) Calculate P[X s 2] 0.30 8(x-3) 3 0.15 8(x-5) 5 X
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![The probability density function of a mixed random variable X is as follows:
af(x)
0.20 8(x)
0.108(+) 0,085(x-1)
XX
a) Find the value of the constant a
b) Calculate P[X s 2]
0.30 8(x-3)
3
0.15 8(x-5)
5
X](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F71f6a4b8-527f-4030-b85a-828002701c6f%2F4aae3303-adf2-4420-9813-9355d1eed7fc%2Fcc24oxw_processed.png&w=3840&q=75)
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- If x is a continuous random variable, then the total area under the probability distribution f(x) for the continuous random variable x is always: A equal to 1. B) between zero and 1. (c) less than1. D greater than 1.The probability density function of the discrete X random variable is given as follows: X 1 4 f(xi) 0.12 0.27 0.31 0.23 0.07 Based on the table above; find the following functions: i) Expected value ii) E([2X3+4]/5) iii)VarianceLet X be a discrete random variable with P(X = -1) = .3, P(X = 1) = .45, P(X = 2) = .15 and P(X = 6) = .1. Find E(X).
- Let X be a discrete random variable with probability mass function given in the following table:a) Consider the following probability density distribution of random variable X. if 052 l l 0.5 If P(A/B)=0.5 and P(B)=0.8, then the 1/1 probability that both A and B occur is O 0.8 O 0.2 O 0.6 0.4 If f(x)=(2x+3)/1O, where 0A random variable X has the following probability mass function for x = 0, 1, 2, 5. Based (PMF): P(X= x) = (x+1) 12 on this PMF, what is P(X≥ 2)? 5/12 1/2 3/4 11/12Q1 Let probability distribution function of Xbe defined by х %3D 0,1, 2, 3. a P(x) = otherwise. Find the value of a. (а) (b) (c) (d) Find P(-1[Q1] The probability distribution of the discrete random variable X is: f(X) = k23-* , for x = 4,5, 6, 7 (a) Find: • the value of the constant k. • The mean E (X). • The variance Var(X). (b) Sketch F(X).Let X be a random variable with pmf P(O)=0.2, P(1)-0.5, P(2)=0.3. Let F(X) be the cdf of X. (a) Find P(X<0.7) (b) Find F(1.3). (c) Find F(3).(Continuous random variable) In a city, the daily electricity consumption (millions of kWh) is a random variable whose probability density is: f(x) - ਵਿਆ = 0 x xe 3 six>0 six<0 The city's electric power plant has a daily capacity of 12 million kWh. a. Verify that the given function is a probability density function. b. Calculate the probability that the power plant cannot meet the demand for electric power.A shop receives a shipment of 1000 lamps. The probability that any individual lamp is defective is 0.2%. Assume the defectiveness is independent of cach lamp. Let X be the number of defective lamps in the batch of 1000. What is the probability mass function of X? O P(X = k) = (00) 0.002* (1 – 0.002)1000 , k = 0,1, 2, ..., 1000 O P(X = k) = 0.002* (1 – 0.002)1000–&, k = 0, 1, 2, .….., 1000 O P(X = k) = (1000) 0.002* (1 – 0.002)1000 , k = 1, 2, ..., 1000 O P(X = k) = (00)0.002100- (1 – 0.002)*, k = 0, 1, 2, ..., 1000SEE MORE QUESTIONSRecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON