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Question # 3 (A) The probability distribution function of a continuous variable is as follows: p(x) k x (1+x2) 0 G1Sx3+1) else where where k is a constant. (i) (ii) (iii) Find the value of, k Find the expected mean and standard deviation Determine the cumulative probability between (-1 that is, P(x+0.5)? x + 0.5); Answer-hints: (iii)i P(x 0.5) 15/16] Indicated below is...
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2 Question # A digitized video-transmission involves streaming of packets wherein the statistics of occurrence of bit-rate from packet-to-packet may strongly depend in values between consequent packets involved; and, this bit-rate (denoting the RV) is considered as of variable bit rate (VBR) type Suppose a test digitized transmission carries a randomly mixed set of such video packets. The statistics of occurrence the packets...
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Question # 4 (A) The life-time of a perishable product specified in months is modeled by a random variable (RV), x with a pdf given by: p(x) = k × (9-x) for 0 otherwise x S9 Here, k is a positive constant. Find: (a) Value of k; and, (b) expected value of the life-time is less than 4 months. life-time; and, (c) probability...
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Question # 1 Voice-transmission involves streaming of packets on a digital communication link wherein the statistics of occurrence of bits in each packet can be considered as of approximately similar bit- rate (constant bit rate (CBR) transmission type). Suppose a mix of such voice packets appears randomly in a grouped set of ten (10) types in a transmission; and, each group indexed as...
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Question # 5 (A) Two identical routers are located at site-A with 8 ports and at site-B with 10 ports. In how many ways can these routers be connected to 5 access points (Aps) placed on the network at the same time? Answer-hints: A and Bare independent. Jointly, they can enable 14,112 connections] (B) A Cisco edge-router in a WAN receives requests for...
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Question # 7 A random variable x has the following distribution: px) 0. -2 -1 0 +1 +2 +3 0.2 k 0.3 2k (i) Find k. (ii) Find P(x <0). (iii) Find P Answer-hints: (iii) P(-2 < x < +2) = 0.8; (v) E11-1.01 2 x +2). (iv) Plot CDF of x; and (v) Find E[x]
Question # 10 A random variable (RV) x is uniformly-distributed from a to b. Given that: p(a sx b) 2 and the median v alue of the RV is equal to: 5. Hence, determine the values of a and b. (Note: The median divides the distribution such that: CDF to its left CDF to its right 0.5) Answer-hints: a-4.75 and b-5.25
please please give step by step instructions i know answer i need know how to do it Let X be a uniformly distributed continuous random variable that lies between 1 and 10. i. Sketch the probability density function for X. ii. Find the formula for the cumulative distribution for X and use it to compute the probability that X is less than 6.
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(1) The pdf namely, fx(x) of a RV, x is distributed as follows: In the range (0x <1) Otherwise ft(x)--x (i) Find the pdf of: y 8x3 in the monotonically increasing in the given range ofxii determine the range ofy; and, (iii) decide the mean of y Answer hint: pdf(y) Ly136) (2) The pdf namely, fx(x) of a RV, x is distributed...
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PROBLEM 16.2 (pg 143,#7) The time X (in minutes) for a lab assistant to prepare the equipment for a certain experiment is known to take anywhere from 10 to 35 minutes. Assume that the probability is uniformly distributed over those times a. The pdf of X is s (x)- . What is the probability that the lab assistant takes c. For any a such that 10 < aa+8 35 (this means less than half...