a)
P(X>=6) =P(first five result are failure) =(1-1/2)^5 =1/32
b)
here mean of distribution=μ=1/p=2 |
varaince =σ2=(1-p)/p2=2
from Markov's inequality: P(X>x) <=E(x)/a
therefore P(X>6) <=2/6
or P(X>6) <=1/3
c)
from Chebychev's inequality: P(X-µ>a) <=Var(x)/(2a2)
P(X>6)=P(X-2>4) <=2/(2*42)
P(X<6) <=1/16
2 5. Suppose X is a discrete random variable that has a geometric distribution with p=...
2 of 3 01- 5. Suppose X is a discrete random variable that has a geometric distribution with p= a. Compute P(X > 6). [5] b. Use Markov's Inequality to estimate P(X > 6). [5] c. Use Chebyshev's Inequality to estimate P(X > 6). (5)
5. Suppose X is a discrete random variable that has a geometric distribution with p= 1. a. Compute P(X > 6). [5] b. Use Markov's Inequality to estimate P(X> 6). [5] c. Use Chebyshev's Inequality to estimate P(X>6). [5] t> 0 6. Let be the probability density function of the continuous 0 t< 0 random variable X. a. Verify that g(t) is indeed a probability density function. [8] b. Find the median of X, i.e. the number m such that...
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please fast and clear A discrete random variable X has the following probability distribution. 2 -1 0.4 0 0.3 f(x) a Find P(X>0). Select one: 0.6 1 0.3 0.5 0.4
Let X be a discrete random variable that follows a Poisson distribution with = 5. What is P(X< 4X > 2) ? Round your answer to at least 3 decimal places. Number
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10) The X random variable has a normal distribution. P(X > 15) = 0.0082 and P(X<5) = 0.6554 find the mean and variance of this distribution
Exercise 2 Consider a random variable X with E]5 and VarX 16 (a) Calculate P(lz-5 < 6) if X follows a normal distribution. (b) Use Chebyshev's inequality to provide a lower bound for P(-5). (No longer assume X is normal.)
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A. Random variable X has a binomial distribution, B(36, 0,5). Use the normal approximation, Compute P[15Kx<19)- B. Random variable X has a normal distribution, N(50, 100) Compute P(X < 41 or X>62.0)