P(X <= 8) = 1 - P(X > 8) = 1 - ( P(X = 9) + P(X = 10)
1 - (10C9 0.3^9 * 0.7 + 0.3^10)
= 1 - (10 * 0.3^9 * 0.7 + 0.3^10)
= 0.999856
b)
P(X = 7)
= 10C7 * 0.3^7 * 0.7^3
= 0.009001
c)
P(X > 6)
= P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)
= 0.009001 + 10C9 0.3^8 *0.7^2 + (10 * 0.3^9 * 0.7 + 0.3^10)
= 0.010592
Problem 2: Let X be a binomially distributed random variable based on n 10 trials with...
The probability mass function of a random variable X is given by Px(n)r n- (a) Find c (Hint: use the relationship that Ση_0 n-e) (b) Now assume λ = 2, find P(X = 0) (c) Find P(X>3)
1. The probability mass function of a random variable X is given by Px(n) bv P Yn (a) Find c (Hint: use the relationship that Σο=0 (b) Now assume λ = 2, find P(X = 0) (c) Find P(X>3) n-0 n! ex)
Suppose that X is a continuous random variable whose probability density function is given by (C(4x sa f(x) - 0 otherwise a) What is the value of C? b) Find PX> 1)
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Let X be an exponentially distributed random variable with parameter λ. Prove that P(X > s + tK > t) P(X > s) for any S,12 0
Let h be an exponentially-distributed random variable with the distribution function p- exp(-x) for x > 0 and ph = nction Ph 0 for a s 0. Derive the distribution function of its square root, Solution: 2y exp(-y2
6. Let X be a normal random variable with mean u = 10. What is the standard deviation o if it is known that p (IX – 101 <>) =
Let X, Y be two independent exponential random variables with means 1 and 3, respectively. Find P(X> Y)
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4.3. Let X and Y be independent random variables uniformly distributed over the interval [θ-, θ + ] for some fixed θ. Show that W X-Y has a distribution that is independent of θ with density function for lwl > 1.