(iii) A random variable has a triangular probability density function with a = 50, b = 375, and m = 250. (a) Sketch the probability distribution function for this random variable. Label the points a = 50, b (i) = f(x) 0.008 0.007 0.006 0.005 0.004 0.003 0.002 0.001 0 0 50 100 150 200 250 300 350 400 X (ii) 0.008 f(x) 0.007- 0.006 0.005 0.004 0.003 0.002 0.001 0 0 50 100 150 200 250 300 350 400 X 375, and m = 250 on the x-axis. Choose the correct graph below. (iii) 0.008 f(x) 0.007 0.006 0.005 0.004 0.003 0.002 0.001 0 0 50 100 150 200 250 300 350 400 X (iv) 0.008 0.007 Graph (i) f(x) 0.006 0.005 0.004 0.003 0.002 0.001 0 0 50 100 150 200 250 300 350 400 X

5. Determine the overall resistance of a 100-meter length of 14 AWA (0.163 cm diameter) wire made of the following materials. a. copper (resistivity = 1.67x10* Q•m) b. silver (resistivity = 1.59x10 Q•m) c. aluminum (resistivity = 2.65x10* Q•m) d. iron (resistivity = 9.71x10* Q•m)

the logit function(given as l(x)) is the log of odds function. what could be the range of logit function in the domain x=[0,1]?

PYTHON PROGRAM Code with comments and output screenshot is must for an Upvote. Do not copy from other websites. Thank you!

A box contains three fair coins, and two trick coins that have heads on both sides.(a) What is the probability that a randomly selected coin from the box will come up heads whenflipped?   (b) Suppose you randomly pick a coin from the box and flip it, and it comes up heads. What is theprobability that it’s one of the trick coins?   (c) Let X be the random variable that represents the number of heads when every coin in the box isflipped. What is the probability distribution of X? (Hint: you can try counting all the outcomes,or you can remember that coin flips are independent of each other.)   (d) What is the expected number of heads when all the coins are flipped?Page 2

True or False: The probability a continuous random variable is near some value is defined by its probability density function.  True  False

algorithms

5 Consider a random variable X which takes values in X= {1, 2, 7} with probabilities as the following table indicates. Consider the two codes wi and w2 defined by the table below X₁ P(X) wi(x) w2(x) X₁ 0.08 1001 010 X₂ 0.21 01 011 X3 0.14 001 000 X₁ 0.04 1000 110 ii. The average codeword length for each code. L(wi) bit/symbol Xs 0.25 11 111 Answer the following: i. Express (into original symbols Xi) the encoded string {000011010111101} using code wi(x). L(w2) bit/symbol X6 0.11 000 101 iii. Explain which code is better for compression applications, and why? X1 0.17 101 001

The spring in the figure below is stretched from its equilibrium position at x = 0 to a positive coordinate xo. ko HINT x = 0 x = xo PE sn PE 50 The force on the spring is F and it stores elastic potential energy PESO. If the spring displacement is tripled to 3x, determine the ratio of the new force to the original force, and the ratio of the new to the original elastic potential energy, Fo Fo PESO (a) the ratio of the new force to the original force, PE ST PE SO (b) the ratio of the new to the original elastic potential energy,

The voltage V(1) (in V) and the current i(t) (in Amp) t seconds after closing the switch in the circuit shown are given by: R Vdt) = V(1– e/) i(t) = e, where t, = RC is the time constant. Consider the case where V = 24 V, R = 3800 2 and C = 4000 x 10-6 F. Determine the voltage and the current during the first 20 s after the switch is closed. Create a vector with values of times from 0 to 20 s with spacing of 2 s, and use it for calculating V(1) and i(t). Display the results in a three-column table where the values of time. voltage and current are displayed in the first, second, and third columns, respectively. (To display values in a Table, just create matrix and have its output displayed) Script ® C Reset I MATLAB Documentation 1 %Don't change the variable name 2 table =