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Consider the following function 2² +6+ for r= 1.2.3, 4. 40 a) Verify that it can...
Question 1. A Discrete Distribution - PME Verify that p(x) is a probability mass function (pmf)...
Question 1. A Discrete Distribution - PME Verify that p(x) is a probability mass function (pmf) and calculate the following for a random variable X with this pmf 1.25 1.5 | 1.7522.45 p(x) 0.25 0.35 0.1 0.150.15 (a) P(X S 2) (b) P(X 1.65) (c) P(X = 1.5) (d) P(X<1.3 or X 221) e) The mean (f) The variance. (g) Sketch the cumulative distribution function (edf). Note that it exhibits jumps and is a right continuous function.
5. Let X be a discrete random variable. The following table shows its possible values r...
5. Let X be a discrete random variable. The following table shows its possible values r and the associated probabilities P(X -f(x) 013 (a) Verify that f(x) is a probability mass function (b) Calculate P(X < 1), P(X < 1), and P(X < 0.5 or X > 2). (c) Find the cumulative distribution function of X ompute the mean and the variance of
2. Let X be a discrete random variable with the following cumulative distribution function 0 0.2...
2. Let X be a discrete random variable with the following cumulative distribution function 0 0.2 0.5 ェ<2, 2-1<5.7, 5.7-1 6.5, 6.5 <エ<8.5, F(z)= 18.5 エ a) Find the probability mass function of X b) Find the probabilities P(x>5), P(4<X 6x> 5) c) If E(X) = 5.76, find c.
2). Consider a discrete random variable X whose cumulative distribution function (CDF) is given by 0...
2). Consider a discrete random variable X whose cumulative distribution function (CDF) is given by 0 if x < 0 0.2 if 0 < x < 1 Ex(x) = {0.5 if 1 < x < 2 0.9 if 2 < x <3 11 if x > 3 a)Give the probability mass function of X, explicitly. b) Compute P(2 < X < 3). c) Compute P(x > 2). d) Compute P(X21|XS 2).
5. Consider the discrete random variable X with probability mass function p.) = (3/30 for r=1...
5. Consider the discrete random variable X with probability mass function p.) = (3/30 for r=1 6/30 for r= 2 8/30 for r=3 7/30 for r = 4 4/30 for r = 5 2/30 for r= 6 10 otherwise. You may find it helpful to use a table with columns for I, Px(), 2. Px(2), and r.Px() to keep track of your computations. Do not round off-express all values as rational fractions. a) Find the probability P(X<3. b) Find the...
Please answer me clearly so I can read well BSP2014 Tutorial 2 1. Check whether the...
Please answer me clearly so I can read well
BSP2014 Tutorial 2 1. Check whether the given function can serve as the probability mass function(p.m.f.) of a random variable 2forx-1,2, 3,4, 5 ii) Ax)for-0,1,2, 3,4 2. A random variable X has the following probability distribution. 0.1 2k 0.3 i)Find k ii)Evaluate PX2 and P-2X2) iii) Find the CDF of X 3. If X has the cumulative distribution function, CDF Fix) = I/2 , 1 xc3 x25 Find a) PXS 3)...
please show you steps, and add some exppanation if possible. Thank you! 5. Let X associated...
please show you steps, and add some exppanation if
possible. Thank you!
5. Let X associated probabilities P(X = x)-/(2) be a discrete random variable. The following table shows its possible values r and the () 2/8 3/8 2/8 1/8 (a) Verify that f(x) is a probability mass function. (b) Calculate P(X < 1), P(X s 1), and P(X0.5 or Xx> 2) (c) Find the cumulative distribution function of X. (d) Compute the mean and the variance of X
5. Let X be a discrete random variable. The following table shows its possible values associated...
5. Let X be a discrete random variable. The following table shows its possible values associated probabilities P(X)( and the f(x) 2/8 3/8 2/8 1/8 (a) Verify that f(x) is a probability mass function. (b) Calculate P(X < 1), P(X 1), and P(X < 0.5 or X >2) (c) Find the cumulative distribution function of X. (d) Compute the mean and the variance of X.
Consider a discrete random variable X with the probability mass function p X ( x )...
Consider a discrete random variable X with the probability mass function p X ( x ) = x/C , x = 3, 4, 5, 6, 7, zero elsewhere. consider Y = g( X ) = 100/(x^2+1) . b) Find the probability distribution of Y.
1. Consider the following Cumulative Distribution Function (CDF) of random variable 0.41 1 t <3 0.78...
1. Consider the following Cumulative Distribution Function (CDF) of random variable 0.41 1 t <3 0.78 3 < t < 5 0.94 5t<7 F(t) = a. 4 Find P(T> 3); P(1.5 < T b. [3] Find E(3T +5) and V (3T5) 6); P(T < 5IT2)
Question 1. A Discrete Distribution - PME Verify that p(x) is a probability mass function (pmf) and calculate the following for a random variable X with this pmf 1.25 1.5 | 1.7522.45 p(x) 0.25 0.35 0.1 0.150.15 (a) P(X S 2) (b) P(X 1.65) (c) P(X = 1.5) (d) P(X<1.3 or X 221) e) The mean (f) The variance. (g) Sketch the cumulative distribution function (edf). Note that it exhibits jumps and is a right continuous function.
5. Let X be a discrete random variable. The following table shows its possible values r and the associated probabilities P(X -f(x) 013 (a) Verify that f(x) is a probability mass function (b) Calculate P(X < 1), P(X < 1), and P(X < 0.5 or X > 2). (c) Find the cumulative distribution function of X ompute the mean and the variance of
2. Let X be a discrete random variable with the following cumulative distribution function 0 0.2 0.5 ェ<2, 2-1<5.7, 5.7-1 6.5, 6.5 <エ<8.5, F(z)= 18.5 エ a) Find the probability mass function of X b) Find the probabilities P(x>5), P(4<X 6x> 5) c) If E(X) = 5.76, find c.
2). Consider a discrete random variable X whose cumulative distribution function (CDF) is given by 0 if x < 0 0.2 if 0 < x < 1 Ex(x) = {0.5 if 1 < x < 2 0.9 if 2 < x <3 11 if x > 3 a)Give the probability mass function of X, explicitly. b) Compute P(2 < X < 3). c) Compute P(x > 2). d) Compute P(X21|XS 2).
5. Consider the discrete random variable X with probability mass function p.) = (3/30 for r=1 6/30 for r= 2 8/30 for r=3 7/30 for r = 4 4/30 for r = 5 2/30 for r= 6 10 otherwise. You may find it helpful to use a table with columns for I, Px(), 2. Px(2), and r.Px() to keep track of your computations. Do not round off-express all values as rational fractions. a) Find the probability P(X<3. b) Find the...
Please answer me clearly so I can read well
BSP2014 Tutorial 2 1. Check whether the given function can serve as the probability mass function(p.m.f.) of a random variable 2forx-1,2, 3,4, 5 ii) Ax)for-0,1,2, 3,4 2. A random variable X has the following probability distribution. 0.1 2k 0.3 i)Find k ii)Evaluate PX2 and P-2X2) iii) Find the CDF of X 3. If X has the cumulative distribution function, CDF Fix) = I/2 , 1 xc3 x25 Find a) PXS 3)...
please show you steps, and add some exppanation if
possible. Thank you!
5. Let X associated probabilities P(X = x)-/(2) be a discrete random variable. The following table shows its possible values r and the () 2/8 3/8 2/8 1/8 (a) Verify that f(x) is a probability mass function. (b) Calculate P(X < 1), P(X s 1), and P(X0.5 or Xx> 2) (c) Find the cumulative distribution function of X. (d) Compute the mean and the variance of X
5. Let X be a discrete random variable. The following table shows its possible values associated probabilities P(X)( and the f(x) 2/8 3/8 2/8 1/8 (a) Verify that f(x) is a probability mass function. (b) Calculate P(X < 1), P(X 1), and P(X < 0.5 or X >2) (c) Find the cumulative distribution function of X. (d) Compute the mean and the variance of X.
1. Consider the following Cumulative Distribution Function (CDF) of random variable 0.41 1 t <3 0.78 3 < t < 5 0.94 5t<7 F(t) = a. 4 Find P(T> 3); P(1.5 < T b. [3] Find E(3T +5) and V (3T5) 6); P(T < 5IT2)
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