Gaussian and Laplacian noise of a signal

I have no idea how to start this problem...

I am looking to generate a baseband transmission scheme that is made of binary rectangular pulses. The transmitted signal is contaminated by additive noise.

By using mean and variance estimators I am to determine the mean and variance using the generated noise with no signal transmitted.

At that point, I look to subtract the estimated mean from the signal yielding a fairly clean signal.

Using that signal I have to use a "detector" (not sure of what this is referring to) to decide whether a 0 or 1 was transmitted. Then compare the received string and transmitted string to determine the number of errors and the average probability of error.

I was told I needed to learn how to generate a Gaussian random variable. After following some examples I have this: (Please advise me if it does not pertain to a solution of problem I mentioned above)

    close all
    clc

    %%Generation of a signal bpsk modulation
    %This takes a set of random numbers and converts them to bits 0's & 1's
    %The 2*X-1 will create -1's in place of the 0's from the bit conversion.
    signal_i = 2*(rand(1,10^5)>0.5)-1;
    signal_q = zeros(1,10^5);

    %In communication systems we have two components
    %which is why we have singal i and q
    scatterplot(signal_i + signal_q);

    %%Combining for complex representation
    signal = complex(signal_i, signal_q);
    p_signal = mean(abs(signal).^2)
    e_signal = (abs(signal).^2);

    %%Adding some noise of a known variance
    for var = 1/50:1/10:0.5
        noise = 1/sqrt(2)*(randn(1,10^5)+j*randn(1,10^5))*sqrt(var);
          addNoise = signal + noise;
          figure(1);
          plot(real(addNoise),imag(addNoise),'b*');
          drawnow('expose');
      end

In the end, I will need to transmit the sequence using two cases with parameters, one Gaussian noise and the other Laplacian.

I was given the sequences of: Equal probabilities: 10001011000111101001 Unequal probabilities: 11001111011011101101

Am I on the right track with the current code vs project requirements? If not, where shall I start?

Thanks in advance.