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E1. Gaussian random variable W is known to have P[W>4] = 1/2. Based on this information, (a) sketch its possible PDF. (b) Now also assume that Var[W] is very small. Refine your sketch in the first part taking into account this new information.E2. We are told that r.v. X has mean value = 10 and variance = 2/3. Draw the pdf of X under the assumption that (a) X is Gaussian, (b) X is continuous and uniform.E3. What would you predict to be the minimum entropy (in bits) of a Bernoulli random variable? Explain.E4. An exponential r.v. B is known to have mean value 5. Write a formula for its PDF:E5. Sketch the approximate PDFs for continuous, zero-mean uniform random variable X when given that (a) E[X2] = 1, and (b) E[X2] = 2.E6. A noisy communication channel distorts a transmitted sequence of pulses (at amplitudes A) by adding to it samples of random variable N (having zero mean and standard deviation N). We learned that an estimated probability of bit transmission error in the channel is Q(A/N). What assumption about r.v. N were made in order to arrive at this estimate?E7. Give a strategy for estimating the CDF of random variable X, when the PDF of X is not known.E8. Samples of a zero-mean, uniformly-distributed continuous r.v. X are passed through a uniform quantizer to produce r.v. Y. (The quantizer range matches the range of X.) What will be the quantization signal-to-noise ratio, in dB, when it is given that there are 100 quantizer output levels?E9. Discrete r.v. Y = 2X + 2, where r.v. X = Bernoulli(1/4). Find Cov[X,Y] by directly evaluating the expectation defining covariance, and then doublecheck your result using an alternate method
Consider the thermal noise produced by a resistor. How does the noise level change if the resistance is increased by a factor of 100 Next, assume the noise is passed through an ideal, noiseless low-pass filter.
Sketch the baseband signals for the two users when user 1 sends the bits 011, and user 2 sends the bits 101. Add the signals for the first bit only, and show that the output of the correlator for user 1 is -4, corresponding to a 0
(a) A Ge bar 0.1 cm long and 100 m2 in cross-sectional area is doped with 1×1017 cm-3 gallium. Find the current at 300 K with 10 V applied. (b) Upon a steady illumination uniform excess carriers are generated in the Ge bar.
the bottom of the conduction band at one end of a silicon resistor is at the same energy level as the top of the valence band at the other end. What current flows through the resistor if the resistance is 1.12k
The discussion must address phase angle relationships of current and voltage. The answer must include the effect of source frequency on the voltage drolps across the resistor and the inductor at very loave and very high frequency values.
Consider a magnetic dipole carrying a current I. a. Calculate the magnetic flux density B at a point P specified in spherical coordinates. Express the answer in terms of the magnetic dipole moment m. Justify all the assumptions adopted.
Find the signal-interference ratio in dB when 120-sectoring antenna is used and the propagation coefficient n =3. If a cluster is replicated 10 times within the system, find the total number of users that can be served with this wireless cellular sy..
A balanced delta connected load of 15 + j18 ohms per phase is connected at the end of a three-phase line. The line impedance is 1 + j2 ohms per phase. The line is supplied from a three-phase source with a line-to-line voltage of 207.85 V rms.
For the system described by the following equations, with the input x(t) and output y(t), determine which are invertible systems and which are noninvertible. For the invertible systems, find the input-output relationships of the inverse system.
What frequency must be used for basis symbols f1 = sin(pi*ct) and f2 = cos(pi*ct) with a symbol period of 1/(9600Hz) to contain 6 cycles of the sin and cos
Given a complete sequential program without any branches (no GOTO and CALL statements) that consists of 12813 instructions and a PIC microcontroller that is connected to a 2.0 MHz external clock/oscillator
Suppose we have a 4Kword memory RAM with each word containing 32 bits. How many address bits and how many output bits are needed. Draw the block diagram of a negative edge-triggered JK FF which is asynchronously set by a 1 and asynchronously reset b..
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